Chapter 6 - Financial Planning
Practice set 6.1
1. Alka spends 90% of the money that she receives every month, and saves Rs. 120. How much money does she get monthly?
Solution:
Let Alka’s monthly income be ₹ x.
Alka spends 90% of the money that she receives every month.
∴ Amount spent by Alka = 90% of x
∴ Amount spent by Alka = \(\large \frac {90}{100}\) × x
∴ Amount spent by Alka = 0.9x
Now,
Savings = Income – Expenditure
∴ 120 = x – 0.9x
∴ 120 = 0.1 x
∴ x = \(\large \frac{120}{0.1}\)
∴ x = \(\large \frac{120\, ×\, 10}{1}\)
∴ x = 1200
Ans: Alka gets ₹1200 monthly.
2. Sumit borrowed a capital of Rs. 50,000 to start his food products business. In the first year he suffered a loss of 20%. He invested the remaining capital in a new sweets business and made a profit of 5%. How much was his profit or loss computed on his original capital ?
Solution:
Original capital borrowed by Sumit = ₹ 50000
Sumit suffered a loss of 20% in his food products business.
∴ Loss suffered in the first year = 20% of 50000
∴ Loss suffered in the first year = \(\large \frac {20}{100}\) × 50000
∴ Loss suffered in the first year = ₹10000
Remaining capital = Original capital – loss suffered
∴ Remaining capital = 50000 – 10000
∴ Remaining capital = ₹ 40000
Sumit invested the remaining capital i.e. ₹ 40,000 in a new sweets business and made a profit of 5%.
∴ Profit in sweets business = 5% of 40000
∴ Profit in sweets business = \(\large \frac {5}{100}\) x 40000
∴ Profit in sweets business = ₹ 2000
New capital with Sumit after the profit in new sweets business = 40000 + 2000 = ₹42000
Now,
New Capital < Original Capital
∴ Sumit suffered a loss.
Total loss on original capital = Original capital – New capital
∴ Total loss on original capital = 50000 – 42000
∴ Total loss on original capital = ₹ 8000
Percentage of Loss = \(\large \frac {Total\, Loss}{Original\, Capital}\) × 100
∴ Percentage of Loss = \(\large \frac {8000}{50000}\) × 100
∴ Percentage of Loss = 16%
Ans: Sumit suffered a loss of 16% on the original capital.
3. Nikhil spent 5% of his monthly income on his children’s education, invested 14% in shares, deposited 3% in a bank and used 40% for his daily expenses. He was left with a balance of Rs. 19,000. What was his income that month?
Solution:
Let the monthly income of Nikhil be ₹ x.
Nikhil invested 14% in shares, deposited 3% in a bank, spent 5% on his children’s education and used 40% for his daily expenses.
∴ Total investment + Total expenditure = (14% + 3% + 5% + 40%) of x
∴ Total investment + Total expenditure = 62% of x
∴ Total investment + Total expenditure = \(\large \frac {62}{100}\) × x
∴ Total investment + Total expenditure = 0.62x
Amount left with Nikhil = Income – (Total investment + Total expenditure)
∴ 19000 = x – 0.62x
∴ 19000 = 0.38x
∴ x = \(\large \frac {19000}{0.38}\)
∴ x = \(\large \frac {19000\, ×\,100}{38}\)
∴ x = 500 × 100
∴ x = ₹ 50000
Ans: The monthly income of Nikhil is ₹ 50000.
4. Mr. Sayyad kept Rs. 40,000 in a bank at 8% compound interest for 2 years. Mr. Fernandes invested Rs. 1,20,000 in a mutual fund for 2 years. After 2 years, Mr. Fernandes got Rs. 1,92,000. Whose investment turned out to be more profitable?
Solution:
For Mr. Sayyad:
Mr. Sayyad kept ₹ 40,000 in a bank at 8% compound interest for 2 years
P = ₹ 40000
R = 8%
n = 2 years
∴ Compound interest = Amount – Principal
∴ Compound interest = P\( \left(1\;+\;\large \frac R{100}\right)^n\) – P
∴ Compound interest = P\( \left[\left(1\;+\;\large \frac R{100}\right)^n\;-\;1\right]\)
∴ Compound interest = 40000\( \left[\left(1\;+\;\large \frac 8{100}\right)^2\;-\;1\right]\)
∴ Compound interest = 40000[(1 + 0.08)² – 1]
∴ Compound interest = 40000[(1.08)² – 1]
∴ Compound interest = 40000[1.1664 – 1]
∴ Compound interest = 40000(0.1664)
∴ Compound interest = ₹1656
∴ Mr. Sayyad’s percentage of profit earned = \(\large \frac {Interest}{Amount\, Invested}\) × 100
∴ Mr. Sayyad’s percentage of profit earned = \(\large \frac {6656}{40000}\) × 100
∴ Mr. Sayyad’s percentage of profit earned = 16.64%
For Mr. Fernandes:
Amount invested by Mr. Fernandes in mutual fund = ₹ 120000
Amount received by Mr. Fernandes after 2 years = ₹ 192000
∴ Profit earned by Mr. Fernandes = Amount received – Amount invested
∴ Profit earned by Mr. Fernandes = 192000 – 120000
∴ Profit earned by Mr. Fernandes = ₹72000
∴ Mr. Fernandes percentage of profit earned = \(\large \frac {Interest}{Amount\, Invested}\) × 100
∴ Mr. Fernandes percentage of profit earned = \(\large \frac {72000}{120000}\) × 100
∴ Mr. Fernandes percentage of profit Interest = 60%
From (i) and (ii),
Investment of Mr. Fernandes turned out to be more profitable.
Ans: Investment of Mr. Fernandes is more profitable.
5. Sameera spent 90% of her income and donated 3% for socially useful causes. If she left with Rs. 1750 at the end of the month, what was her actual income?
Solution:
Let the actual income of Sameera be ₹ x.
Sameera spent 90% of her income and donated 3%.
∴ Sameera’s total expenditure = (90% + 3%) of x
∴ Sameera’s total expenditure = 93% of x
∴ Sameera’s total expenditure = \(\large \frac {93}{100}\) × x
∴ Sameera’s total expenditure = 0.93x
Now,
Savings = Income – Expenditure
∴ 1750 = x – 0.93x
∴ 1750 = 0.07x
∴ x = \(\large \frac {1750}{0.07}\)
∴ x = \(\large \frac {1750\, ×\,100}{7}\)
∴ x = 250 × 100
∴ x = 25000
Ans: The actual income of Sameera is ₹ 25000.
∴ Compound interest = P\( \left(1\;+\;\large \frac R{100}\right)^n\) – P
∴ Compound interest = P\( \left[\left(1\;+\;\large \frac R{100}\right)^n\;-\;1\right]\)
∴ Compound interest = 40000\( \left[\left(1\;+\;\large \frac 8{100}\right)^2\;-\;1\right]\)
Practice set 6.2
(1) Observe the table given below. Check and decide, whether the individuals have to pay income tax.
| S. No. | Individuals | Age | Taxable Income (₹) | Will have to pay income tax or not |
|---|---|---|---|---|
(i) | Miss Nikita | 27 | ₹ 2,34,000 | |
(ii) | Mr. Kulkarni | 36 | ₹ 3,27,000 | |
(iii) | Miss Mehta | 44 | ₹ 5,82,000 | |
(iv) | Mr. Bajaj | 64 | ₹ 8,40,000 | |
(iv) | Mr. Desilva | 81 | ₹ 4,50,000 |
(i) Solution:
Miss Nikita’s age = 27 years (< 60 years)
Miss Nikita’s income = ₹ 2,34,000
Miss Nikita’s income is below the basic
exemption limit of ₹ 2,50,000.
∴ Miss Nikita will not have to pay income tax.
(ii) Solution:
Mr. Kulkarni’s age is 36 years (< 60 years)
Mr. Kulkarni’s income = ₹3,27,000
Mr. Kulkarni’s income is above the basic exemption Limit of ₹2,50,000.
∴ Mr. Kulkarni will have to pay income tax.
(iii) Solution:
Miss Mehta’s age = 44 years (< 60 years)
Miss Mehta’s income = ₹5,82,000
Miss Mehta’s income is above the basic exemption limit of ₹2,50,000.
∴ Miss Mehta will have to pay income tax.
(iv) Solution:
Mr. Bajaj’s age = 64 years (Age 60 to 80 years)
Mr. Bajaj’s income = ₹8,40,000
Mr. Bajaj’s income is above the basic exemption Limit of ₹3,00,000.
∴ Mr. Bajaj will have to pay income tax.
(v) Solution:
Mr. Desilva’s age = 81 years (> 80 years)
Mr. Desilva’s income = ₹4,50,000
Mr. Desilva’s income is below the basic exemption limit of ₹ 5,00,000.
∴ Mr. Desilva will not have to pay income tax.
| S. No. | Individuals | Age | Taxable Income (₹) | Will have to pay income tax or not |
|---|---|---|---|---|
(i) | Miss Nikita | 27 | ₹ 2,34,000 | No |
(ii) | Mr. Kulkarni | 36 | ₹ 3,27,000 | Yes |
(iii) | Miss Mehta | 44 | ₹ 5,82,000 | Yes |
(iv) | Mr. Bajaj | 64 | ₹ 8,40,000 | Yes |
(iv) | Mr. Desilva | 81 | ₹ 4,50,000 | No |
(2) Mr. Kartarsingh (age 48 years) works in a private company. His monthly income after deduction of allowances is Rs. 42,000 and every month he contributes Rs. 3000 to GPF. He has also bought Rs. 15,000 worth of NSC (National Savings Certificate) and donated Rs. 12,000 to the PM’s Relief Fund. Compute his income tax.
Solution:
Mr. Kartarsingh’s monthly income = ₹ 42,000
∴ Mr. Kartarsingh’s yearly income = 42,000 × 12 months
∴ Mr. Kartarsingh’s yearly income = ₹ 5,04,000
Mr. Kartarsingh’s monthly contribution to GPF = ₹ 3000
∴ Mr. Kartarsingh’s annual contribution to GPF = 3000 × 12 months
∴ Mr. Kartarsingh’s annual contribution to GPF = 36,000
Mr. Kartarsingh’s investment = Annual contribution to GPF + Cost of NSC
∴ Mr. Kartarsingh’s investment = 36,000 + 15,000
∴ Mr. Kartarsingh’s investment = ₹ 51,000
Donation to PM’s relief fund = ₹ 12, 000
∴ Taxable income = Yearly income – (Investment + Donation to PM’s relief fund)
∴ Taxable income = 5,04,000 – (51,000 + 12,000)
∴ Taxable income = 5,04,000 – 63,000
∴ Taxable income = ₹ 4,41,000
Mr. Kartarsingh income falls in the slab 2,50,001 to 5,00,000.
∴ Income tax = 5% of (Taxable income – 250000)
∴ Income tax = 5% of (4,41,000 – 2,50,000)
∴ Income tax = \(\large \frac {5}{100}\) × 1,91,000
∴ Income tax = 5 × 1910
∴ Income tax = ₹ 9550
Education cess = 2% of income tax
∴ Education cess = \(\large \frac {2}{100}\) × 9550
∴ Education cess = 2 × 95.5
∴ Education cess = ₹ 191
Secondary and Higher Education cess = 1% of income tax
∴ Secondary and Higher Education cess = \(\large \frac {1}{100}\) x 9550
∴ Secondary and Higher Education cess = ₹ 95.50
Total income tax = Income tax + Education cess + Secondary and higher education cess
∴ Total income tax = 9550 + 191 + 95.50
∴ Total income tax = ₹ 9836.50
Ans: Mr. Kartarsingh’s income tax is ₹ 9836.50.
Problem set 6
(1) Write the correct alternative answer for each of the following questions.
(i) For different types of investments what is the maximum permissible amount under section 80C of income tax ?
(A) 1,50,000 rupees
(B) 2,50,000 rupees
(C) 1,00,000 rupees
(D) 2,00,000rupees
OPTION (A) : 1,50,000 rupees
(ii) A person has earned his income during the financial year 2017-18. Then his assessment year is ….
(A) 2016-17
(B) 2018-19
(C) 2017-18
(D) 2015-16
OPTION (B) : 2018-19
(2) Mr. Shekhar spends 60% of his income. From the balance he donates Rs. 300 to an orphanage. He is then left with Rs. 3,200. What is his income ?
Solution:
Let the income of Shekhar be ₹ x
Shekhar spends 60% of his income
∴ Shekhar’s expenditure = 60% of x
Amount remaining with Shekhar = (100 – 60)% of x
∴ Amount remaining with Shekhar = 40% of x
∴ Amount remaining with Shekhar = \(\large \frac {40}{100}\) × x
∴ Amount remaining with Shekhar = 0.4x
From the balance, he donates ₹ 300 to an orphanage
∴ Amount left with Shekhar = 0.4x – 300
But,
Amount left with him is ₹ 3200
∴ 3200 = 0.4x – 300
∴ 0.4x = 3200 + 300
∴ 0.4x = 3500
∴ x = \(\large \frac {3500}{0.4}\)
∴ x = \(\large \frac {3500\, ×\, 10}{4}\)
∴ x = \(\large \frac {35000}{4}\)
∴ x = 8750
Ans: The income of Mr. Shekhar is ₹ 8750.
(3) Mr. Hiralal invested Rs. 2,15,000 in a Mutual Fund. He got Rs. 3,05,000 after 2 years. Mr. Ramniklal invested Rs. 1,40,000 at 8% compound interest for 2 years in a bank. Find out the percent gain of each of them. Whose investment was more profitable ?
Solution:
For Mr. Hiralal:
Amount invested by Mr. Hiralal in mutual fund = ₹ 2,15,000
Amount received by Mr. Hiralal = ₹ 3,05,000
Mr. Hiralal’s profit = Amount received – Amount invested
∴ Mr. Hiralal’s profit = 305000 – 215000
∴ Mr. Hiralal’s profit = ₹ 90000
Mr. Hirala’s percentage of profit = \(\large \frac {90000}{215000}\) × 100
∴ Mr. Hirala’s percentage of profit = \(\large \frac {90000}{2150}\)
∴ Mr. Hirala’s percentage of profit = 41.86%
For Mr. Ramniklal:
P = ₹ 140000
R = 8%
n = 2 years
∴ Compound interest = Amount – Principal
∴ Compound interest = P\( \left(1\;+\;\large \frac R{100}\right)^n\) – P
∴ Compound interest = P\( \left[\left(1\;+\;\large \frac R{100}\right)^n\;-\;1\right]\)
∴ Compound interest = 140000\( \left[\left(1\;+\;\large \frac 8{100}\right)^2\;-\;1\right]\)
∴ Compound interest = 140000[(1 + 0.08)² – 1]
∴ Compound interest = 140000[(1.08)² – 1]
∴ Compound interest = 140000[1.1664 – 1]
∴ Compound interest = 140000(0.1664)
∴ Compound interest = ₹ 23296
∴ Mr. Ramniklal’s percentage of profit = \(\large \frac {23296}{140000}\) × 100
∴ Mr. Ramniklal’s percentage of profit = \(\large \frac {23296}{1400}\)
∴ Mr. Ramniklal’s percentage of profit = 16.64%
Ans: The percentage gains of Mr. Hiralal and Mr. Ramniklal are 41.86% and 16.64% respectively and Mr. Hiralal’s investment was more profitable.
(4) At the start of a year there were Rs. 24,000 in a savings account. After adding Rs. 56,000 to this the entire amount was invested in the bank at 7.5% compound interest. What will be the total amount after 3 years ?
Solution:
P = 24000 + 56000 = ₹ 80000
R = 7.5%
n = 3 years
∴ Total amount after 3 years = P\( \left(1\;+\;\large \frac R{100}\right)^n\)
∴ Total amount after 3 years = 8000\( \left(1\;+\;\large \frac {7.5}{100}\right)^3\)
∴ Total amount after 3 years = 80000 (1 + 0.075)³
∴ Total amount after 3 years = 80000 (1.075)³
∴ Total amount after 3 years = 80000 × 1.242297
∴ Total amount after 3 years = 99383.76
Ans: The total amount after 3 years is ₹ 99383.76.
(5) Mr. Manohar gave 20% part of his income to his elder son and 30% part to his younger son. He gave 10% of the balance as donation to a school. He still had Rs. 1,80,000 for himself. What was Mr. Manohar’s income?
Solution:
Let the income of Mr. Manohar be ₹ x
Amount given to elder son = 20% of x
Amount given to younger son = 30% of x
Total amount given to both sons = (20 + 30)% of x
∴ Total amount given to both sons = 50% of x
∴ Amount remaining with Mr. Manohar = (100 – 50)% of x
∴ Amount remaining with Mr. Manohar = 50% of x
∴ Amount remaining with Mr. Manohar = \(\large \frac {50}{100}\) × x
∴ Amount remaining with Mr. Manohar = 0.5x
Now,
He gave 10% of the balance income as donation to a school
∴ Amount donated to school = 10% of 0.5x
∴ Amount donated to school = \(\large \frac {10}{100}\) × 0.5x
∴ Amount donated to school = 0.05x
And,
Amount remaining with Mr. Manohar after donating to school = 0.5x – 0.05x
∴ Amount remaining with Mr. Manohar after donating to school = 0.45x
Mr. Manohar still have ₹1,80,000 left after donating to school
∴ 180000 = 0.45x
∴ x = \(\large \frac {180000}{0.45}\)
∴ x = \(\large \frac {180000\, ×\, 100}{45}\)
∴ x = \(\large \frac {18000000}{45}\)
∴ x = ₹ 4,00,000
Ans: The income of Mr. Manohar is ₹4,00,000.
(6*) Kailash used to spend 85% of his income. When his income increased by 36% his expenses also increased by 40% of his earlier expenses. How much percentage of his earning he saves now?
Solution:
Let the income of Kailash be ₹ x.
Kailash spends 85% of his income.
∴ Kailash’s expenditure = 85% of x
∴ Kailash’s expenditure = \(\large \frac {85}{100}\) × x
∴ Kailash’s expenditure = 0.85 x
Kailash’s income increased by 36%
∴ Kailash’s new income = x + 36% of x
∴ Kailash’s new income = x + \(\large \frac {36}{100}\) × x
∴ Kailash’s new income = x + 0.36x
∴ Kailash’s new income = 1.36x
Kailash’s expenses increased by 40%
∴ Kailash’s new expenditure = 0.85x + 40% of 0.85x
∴ Kailash’s new expenditure = 0.85x + \(\large \frac {40}{100}\) × 0.85x
∴ Kailash’s new expenditure = 0.85x + 0.4 × 0.85x
∴ Kailash’s new expenditure = 0.85x (1 + 0.4)
∴ Kailash’s new expenditure = 0.85x × 1.4
∴ Kailash’s new expenditure = 1.19x
∴ Kailash’s new saving = Kailash’s new income – Kailash’s new expenditure
∴ Kailash’s new saving = 1.36x – 1.19x
∴ Kailash’s new saving = 0.17x
Percentage of Kailash’s new saving
∴ Percentage of Kailash’s new saving = \(\large \frac {0.17x}{1.36x}\) × 100
∴ Percentage of Kailash’s new saving = 12.5%
Ans: Kailash saves 12.5% of his new earning.
(7*) Total income of Ramesh, Suresh and Preeti is 8,07,000 rupees. The percentages of their expenses are 75%, 80% and 90% respectively. If the ratio of their savings is 16 : 17 : 12, then find the annual saving of each of them.
Solution:
Let the annual income of Ramesh, Suresh and Preeti be ₹ x, ₹ y and ₹ z respectively.
Total income of Ramesh, Suresh and Preeti = ₹ 8,07,000
∴ x + y + z = 807000 …(i)
Percentage of Expenses of Ramesh is 75% of x
∴ Percentage of Savings of Ramesh = 25% of x
∴ Percentage of Savings of Ramesh = ₹ \(\large \frac {25x}{100}\) …(ii)
Percentage of Expenses of Suresh is 80% of y
∴ Percentage of Savings of Suresh = 20% of y
∴ Percentage of Savings of Suresh = ₹ \(\large \frac {20y}{100}\) …(iii)
Percentage of Expenses of Preeti is 90% of z
∴ Percentage of Savings of Preeti = 10% of z
∴ Percentage of Savings of Preeti = ₹ \(\large \frac {10z}{100}\) …(iv)
Now,
Ratio of their savings = 16 : 17 : 12
Let the common multiple be k.
Savings of Ramesh = ₹ 16k …(v)
Savings of Suresh = ₹ 17k …(vi)
Savings of Preeti = ₹ 12k …(vii)
\(\large \frac {25x}{100}\) = 16k …[From (ii) and (v)]]
∴ \(\large \frac {x}{4}\) = 16k
∴ x = 16k × 4
∴ x = 64k …(viii)
\(\large \frac {20y}{100}\) = 17k …[From (iii) and (vi)]]
∴ \(\large \frac {y}{5}\) = 17k
∴ y = 17k × 5
∴ y = 85k …(ix)
\(\large \frac {10z}{100}\) = 12k …[From (iv) and (vii)]]
∴ \(\large \frac {z}{10}\) = 12k
∴ z = 12k × 10
∴ z = 120k …(x)
From (i), (viii), (ix) and (x), we get
64k + 85k + 120k = 807000
269k = 807000
k = \(\large \frac {807000}{269}\)
k = 3000
So,
Annual saving of Ramesh = 16k
Annual saving of Ramesh = 16 x 3000
Annual saving of Ramesh = ₹ 48,000
Annual saving of Suresh = 17k
Annual saving of Suresh = 17 x 3000
Annual saving of Suresh = ₹ 51,000
Annual saving of Preeti = 12k
Annual saving of Preeti = 12 x 3000
Annual saving of Preeti = ₹ 36,000
Ans: The annual savings of Ramesh, Suresh and Preeti are ₹ 48,000, ₹ 51,000 and ₹ 36,000 respectively.
(8) Compute the income tax payable by following individuals.
(i) Mr. Kadam who is 35 years old and has a taxable income of Rs. 13,35,000.
Solution:
Mr. Kadam is 35 years old and his taxable income is ₹13,35,000.
Mr. Kadam’s income is more than ₹ 10,00,000.
∴ Income tax = ₹1,12,500 + 30% of (taxable income – 10,00,000)
∴ Income tax = ₹ 1,12,500 + 30% of (13,35,000 – 10,00,000)
∴ Income tax = 1,12,500 + \(\large \frac {30}{100}\) × 3,35,000
∴ Income tax = 1,12,500 + 1,00,500
∴ Income tax = ₹ 2,13,000
Education cess = 2% of income tax
∴ Education cess = \(\large \frac {2}{100}\) × 2,13,000
∴ Education cess = ₹ 4260
Secondary and Higher Education cess
∴ Secondary and Higher Education cess = 1% of income tax
∴ Secondary and Higher Education cess = \(\large \frac {1}{100}\) × 2,13,000
∴ Secondary and Higher Education cess = ₹ 2130
Total income tax = Income tax + Education cess + Secondary and higher education cess
∴ Total income tax = 2,13,000 + 4260 + 2130
∴ Total income tax = ₹ 2,19,390
Ans: Mr. Kadam will have to pay income tax of ₹ 2,19,390.
(ii) Mr. Khan is 65 years of age and his taxable income is Rs. 4,50,000.
Solution:
Mr. Khan is 65 years old and his taxable income is ₹ 4,50,000.
Mr. Khan’s income falls in the slab ₹ 3,00,001 to ₹ 5,00,000.
Income tax = 5% of (taxable income – 3,00,000)
∴ Income tax = 5% of (4,50,000 – 3,00,000)
∴ Income tax = \(\large \frac {5}{100}\) x 1,50,000
∴ Income tax = ₹ 7500
Education cess = 2% of income tax
∴ Education cess = \(\large \frac {2}{100}\) x 7500
∴ Education cess = ₹ 150
Secondary and Higher Education cess = 1 % of income tax
∴ Secondary and Higher Education cess = \(\large \frac {1}{100}\) x 7500
∴ Secondary and Higher Education cess = ₹ 75
Total income tax = Income tax + Education cess + Secondary and higher education cess
∴ Total income tax = 7500 + 150 + 75
∴ Total income tax = ₹ 7725
Ans: Mr. Khan will have to pay income tax of ₹7725.
(iii) Miss Varsha (Age 26 years) has a taxable income of Rs. 2,30,000.
Solution
Taxable income = ₹2,30,000
Age = 26 years
The yearly income of Miss Varsha is less than ₹ 2,50,000.
∴ Miss Varsha will not have to pay income tax.
Ans: Miss Varsha will not have to pay income tax.