Practice Questions for Simple & Compound Interest

1. CRE 4 - Installments | Simple & Compound Interest

A loan is discharged in three equal annual installments of Rs. 1331 each, if the rate of interest is 10%, find the amount of loan.

(a)
Rs. 3310
(b)
Rs. 3400
(c)
Rs. 3010
(d)
Rs. 3710

2. CRE 4 - Installments | Simple & Compound Interest

A sum of money Rs. 9450 is borrowed at 10% p.a. C.I. The sum is to be paid back in two equal yearly installments. Find the amount of each installment.

(a)
Rs. 5600
(b)
Rs. 5445
(c)
Rs. 5544
(d)
Rs. 5800

Answer: Option B

Explanation :

Let the yearly installment = Rs. x

Amount in 1 years =9450 $(1 + \frac{10}{100})$ =1039.5

Balance = 10395 – x

Amount after 2nd year = (10395 – x) $(1 + \frac{10}{100})$

Now, (10395 – x) $(\frac{110}{100})$ =x⇒x=5445

Hence, option (b).

3. CRE 4 - Installments | Simple & Compound Interest

A woman borrows Rs.4000 from a bank at 7.50% CI. At the end of every year, she pays Rs.1500 as a part repayment of loan and interest. How much does she still owe to the bank after three such installments?

(a)
Rs. 123.25
(b)
Rs. 125
(c)
Rs. 400
(d)
Rs. 469.18

Answer: Option A

Explanation :

Amount remaining after:

1 yr = 4000 $(1 + \frac{7.5}{100})$ - 1500 = 2800

2 yr = 2800 $(1 + \frac{7.5}{100})$ - 1500 = 1510

3 yr = 1510 $(1 + \frac{7.5}{100})$ - 1500 = 123.25

Hence, option (a).

4. CRE 4 - Installments | Simple & Compound Interest

An amount of Rs. 12,820 due 3 years hence, is fully repaid in three annual instalments starting after 1 year The first instalment is 1/2 the second instalment and the second instalment is 2/3 of the third instalment. If the rate of interest is 10% per annum, find the first installment.

(a)
2400
(b)
1800
(c)
2000
(d)
2500

Answer: Option C

Explanation :

Let the third installment be x

⇒ 2nd installment = 2x/3 and 3rd installment = x/3

⇒ 12,820 = $\frac{x}{3} \times 1 . 1^{2} + \frac{2 x}{3} \times 1.1 + x = \frac{6.41 x}{3}$

⇒ x = 6000

∴ 1st installment = x/3 = 2000

Hence, option (c).

5. CRE 4 - Installments | Simple & Compound Interest

A Sonata watch is sold for Rs. 440 cash or for Rs. 200 cash down payment together with Rs. 244 to be paid after one month. Find the rate of interest charged in the installment scheme

(a)
10%
(b)
15%
(c)
20%
(d)
25%

Answer: Option C

Explanation :

Principal for next month = 440 – 200 = 240

Amount paid after next month = 244

Therefore, interest charged at 240 = 4

∴ 4 = $\frac{240 \times r \times 1}{12 \times 100}$

R = 20% per annum

Hence, option (c).

6. CRE 4 - Installments | Simple & Compound Interest

A man borrows Rs. 12,500 at 20% compound interest. At the end of every year he pays Rs. 2000 as part repayment. How much does he still owe after three such instalments?

(a)
12,000
(b)
12,864
(c)
15,600
(d)
None of these

Answer: Option D

Explanation :

Balance = $[\{12500 \times {(1 + \frac{20}{100})}^{3}\} - \{2000 \times {(1 + \frac{20}{100})}^{2} + 2000 \times (1 + \frac{20}{100}) + 2000\}] \Rightarrow [(12500 \times \frac{5}{6} \times \frac{6}{5} \times \frac{6}{5}) - (2000 \times \frac{6}{5} \times \frac{6}{5} + 2000 \times \frac{6}{5} + 2000)] = [21600 - (2880 + 2400 + 2000)] = 14320$

Hence, option (d)

7. CRE 4 - Installments | Simple & Compound Interest

A person borrowed Rs. 5000 from his friend, the understanding being that the money would be returned after 3 years with C.I. 6% p.a. He wanted to return the sum due 1.5 years before it was due. What amount would discharge the debt?

(a)
Rs. 5401
(b)
Rs. 5459
(c)
Rs. 5621
(d)
Rs. 5584

Answer: Option B

Explanation :

A = 5000 ${(1 + \frac{6}{100})}^{1} \times (1 + \frac{6 \times \frac{1}{2}}{100})$ = 5000 × 1.06 × 1.03 = 5459

Hence, option (b).

8. CRE 4 - Installments | Simple & Compound Interest

A man borrowed a sum of money at the beginning of every year at 10% C.I. If at the end of 3 years he pays Rs. 7282, how much did he borrow every year?

(a)
Rs. 2000
(b)
Rs. 2200
(c)
Rs. 2400
(d)
Rs. 1800

Answer: Option A

Explanation :

Let P = Sum borrowed every year

The amount P borrowed at the beginning of 1^st year will become at the end $P {(1 + \frac{10}{100})}^{3}$ of 3^rd year.

The amount P borrowed at the beginning of 2^nd year will become at the end $P {(1 + \frac{10}{100})}^{2}$ of 3^rd year.

The amount P borrowed at the beginning of 3^rd year will become at the end $P (1 + \frac{10}{100})$ of 3^rd year.

Now, $P {(1 + \frac{10}{100})}^{3} + P {(1 + \frac{10}{100})}^{2} + P (1 + \frac{10}{100})$ = 7282

⇒ P = 2000

Hence, option (a).

9. CRE 4 - Installments | Simple & Compound Interest

What annual investment will discharge a debt of Rs. 13,440 due in 4 years at 8% p.a.

(a)
Rs. 3150
(b)
Rs. 3100
(c)
Rs. 3200
(d)
Rs. 3000

Answer: Option D

Explanation :

Let x = annual payment

Now, (amount of x for 3 years) + (amount of x for 2 years) + (amount of x for 1 year) + x = 13,440

$\Rightarrow (x + \frac{x \times 3 \times 8}{100}) + (x + \frac{x \times 2 \times 8}{100}) + (x + \frac{x \times 8}{100}) + x =$ 13440

⇒ 1.24x + 1.16x + 1.08x + x = 13,440

⇒ 4.48x = 13,440

⇒ x = 3000

Hence, option (d).

10. CRE 4 - Installments | Simple & Compound Interest

Samsung mobile phone is available for Rs.2500 cash or Rs.520 cash down payments followed by 4 equal installments. If the rate of interest charged is 25% per annum Simple interest, calculate the monthly installment

(a)
520
(b)
480
(c)
550
(d)
None of these

Answer: Option A

Explanation :

Balance price to be paid in installments = Rs.1980

At the rate of r% per annum after 4 months, Rs.1980 will amount to Rs.

$\frac{P \times R \times T}{100 \times 12}$ = 1980 + $\frac{1980 \times 4 \times 25}{12 \times 100}$ = 2145 ...(1)

Now, the total amount for the 4 installments at the end of fourth month will be $(x + \frac{25 x + 3}{12 \times 100}) + (x + \frac{25 x + 2}{12 \times 100}) + (x + \frac{25 x + 1}{12 \times 100}) + x = 4 x + \frac{25 x}{1200} (1 + 2 + 3 +) = \frac{33 x}{8}$ ...(2)

From (1) and (2), Rs.2145 = 33x/8

⇒ x = Rs.520

Hence, option (a).

CRE 4 - Installments | Simple & Compound Interest

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