Arithmetic

Simple & Compound Interest

Medium

Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is

20860

20808

20480

20640

✅ Correct Option: 2

Anil: Rs 22000 for 6 years at 4% compounded half-yearly

Sunil: Unknown amount for 5 years at 4% compounded half-yearly, then reinvest everything for 1 year at 10% simple interest. Both end up with equal amounts after 6 years

Rate adjustment: 4% per year → 2% per half-year period

Time adjustment: 6 years → 12 half-year periods

Using compound interest formula: $A = P(1 + \frac{r}{100})^n$

Where:

P = Rs 22000 (principal)

r = 2% (rate per half-year)

n = 12 (number of half-year periods)

Anil's final amount = $22000 \times (1 + \frac{2}{100})^{12}$

= $22000 \times (1.02)^{12}$

Finding Sunil's final amount:

Let Sunil's initial investment = P

Phase 1 (Years 1-5): Compound Interest

Rate = 2% per half-year

Time = 10 half-year periods

Amount after 5 years = $P \times (1.02)^{10}$

Phase 2 (Year 6): Simple Interest

Principal for year 6 = $P \times (1.02)^{10}$

Rate = 10% per year

Time = 1 year

Using simple interest formula: $A = P(1 + \frac{rt}{100})$

Final amount = $P \times (1.02)^{10} \times (1 + \frac{10 \times 1}{100})$

= $P \times (1.02)^{10} \times (1.1)$

Since both final amounts are equal:

$22000 \times (1.02)^{12} = P \times (1.02)^{10} \times (1.1)$

$\frac{22000 \times (1.02)^{12}}{(1.02)^{10}} = \frac{P \times (1.02)^{10} \times (1.1)}{(1.02)^{10}}$

$22000 \times (1.02)^2 = P \times (1.1)$

$(1.02)^2 = 1.02 \times 1.02 = 1.0404$

$22000 \times 1.0404 = P \times 1.1$

$22888.8 = P \times 1.1$

Therefore: $P = \frac{22888.8}{1.1} = 20808$

Answer: Sunil's initial investment = Rs 20808

CAT 2024 Slot 1

An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is

CAT 2020 Slot 2

For the same principal amount, the compound interest for two years at $5\%$ per annum exceeds the simple interest for three years at $3\%$ per annum by Rs. $1125$ . Then the principal amount in rupees is

CAT 2019 Slot 1

A person invested a total amount of Rs $15$ lakh. A part of it was invested in a fixed deposit earning $6\%$ annual interest, and the remaining amount was invested in two other deposits in the ratio $2: 1$ , earning annual interest at the rates of $4\%$ and $3\%$ , respectively. If the total annual interest income is Rs $76000$ then the amount (in Rs lakh) invested in the fixed deposit was

CAT 2021 Slot 3

Bank $A$ offers $6 \%$ interest rate per annum compounded half yearly. Bank $B$ and Bank $C$ offer simple interest but the annual interest rate offered by Bank $C$ is twice that of Bank $B$ . Raju invests a certain amount in Bank B for a certain period and Rupa invests $₹ 10,000$ in Bank $C$ for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in Bank $A$ for one year. The interest accrued, in INR, to Rupa is

CAT 2019 Slot 2

Amal invests Rs $12000$ at 8% interest, compounded annually, and Rs $10000$ at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at $7.5 \%$ simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is

CAT 2019 Slot 1

Amala, Bina, and Gouri invest money in the ratio $3: 4: 5$ in fixed deposits having respective annual interest rates in the ratio $6: 5:4$ . What is their total interest income (in Rs) after a year, if Bina's interest income exceeds Amala's by Rs $250$ ?

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)