Question

mrs. reeta deposited a sum of 8400 in a bank. after 2 years, she withdrew 5200 and at the end of 4 years, she received 5288. find the rate of simple interest

Answer 1

Mrs. Geeta deposited a sum of 8400 in a bank.
so, principal , P = 8400 Rs.
Simple interest after 2 years where interest rate r % per annum is given by
S.I = 8400 × r × 2/100 = 168r

so, total amount after 2 years , A = 8400 + 168r

now, Geeta withdraw 5200 from her account.
rest amount = 8400 + 168r - 5200 = 3200 + 168r

for second case,
rest total amount , A = 3200 + 168r
but we know, simple interest is applied only on initial principal amount not whole amount. otherwise it will be compound interest.
so, principal , P = 3200
time taken , t = 4 years
simple interest after (4-2)=2 years , S.I' = 3200 × r × 2/100 = 64r

she received in last 5288
so, 168r + 64r + 3200 = 5288
232r = 5288 - 3200 = 2088
r = 2088/232 = 9%

hence, interest rate is 9%

Answer 2

We will assume R to be the rate of Simple Interest.

Principal for 1st two years = Rs 8400

Simple interest for the 1st two years would be I₁ = P x R x T/ 100

I₁ = 8400 x R x 2/100

I₁ = Rs (168R)

Now when Reeta would  withdraw Rs 5200 after around two years.

So the principal for the next 2 years would be =

Rs 8400 - Rs 5200

= Rs 3200

Then Simple interest for next two years = I₂ = P x R x T/ 100

I₂ = 3200 x R x 2/100

I₂ = Rs 64 R

I₁ + I₂ + 3200 = 5288

168R + 64R = 5288 - 3200

232R = 2088

R = 2088/23

= 9%