Question

A sum invested at 16% p.a. simple interest earns Rs. 736 as interest. If the same sum were kept for 8 more years, the interest would be Rs. 3680. What amount is obtained if the same sum is invested at 9% p.a. compounded annually for 2 years?

• A. Rs. 2732.63
• B. Rs. 2720.75
• C. Rs. 2714.00
• D. Rs. 2845.26

Hint:

Work out the simple interest earned in a single year first, then use that to find the principal before compounding it year by year.

Answer 1

The Correct Option is A

Step 1: Extending the investment by 8 more years adds interest $=3680-736=2944$ for those 8 years. Since simple interest accrues uniformly each year, the annual SI amount $=\dfrac{2944}{8}=368$ per year.
Step 2: Annual SI $=\dfrac{P\times\text{rate}}{100}$, so $368=\dfrac{P\times16}{100}\Rightarrow P=\dfrac{368\times100}{16}=2300$.
Step 3: Check: the original interest of 736 at 368/year corresponds to $t=\dfrac{736}{368}=2$ years, a valid original time period.
Step 4: Now grow $P=2300$ at 9% p.a. compounded annually for 2 years, year by year: Year 1 interest $=2300\times\frac{9}{100}=207$, amount after Year 1 $=2300+207=2507$.
Step 5: Year 2 interest $=2507\times\frac{9}{100}=225.63$, amount after Year 2 $=2507+225.63=2732.63$.
\[\boxed{\text{Rs. }2732.63}\]