Question

A housewife deposited Rs 10,000 on saving account at 5% p.a. interest compounded
yearly and another sum on fixed deposit account at 8% p.a. interest compounded
half yearly. After one year the interest on fixed deposit account
was Rs 152.80 more
than the interest on the saving account, find the total amount of money in her two
accounts at the end of the year.​

Answer 1

Answer:

Rs. 3923.08

Step-by-step explanation:

First principal invested = Rs. 10000

Interest rate = 5%

The interest is compounded yearly.

Time = 1 year

1 year compound interest is equal to simple interest.

Formula for simple interest:

$SI = \dfrac{PRT}{100}$

Interest on first sum = $\frac{10000\times 5\times 1}{100} = Rs\ 500$

Another sum is on fixed deposit 8% compounded half yearly.

Let the sum = Rs $x$

Formula for compound interest is given as:

$CI = P(1+\frac{R}{100})^T - P$

It is compounded half - yearly, therefore T = 2

$CI = x (1+\frac{8}{100})^2 - x\\\Rightarrow CI = x(1.08)^2-x = 0.1664x$

As per question statement:

$0.1664x - 500 = 152.80\\\Rightarrow x = \dfrac{652.80}{0.1664} = Rs\ 3823.08$