Question

A man borrowed Rs 18,000 for 2 years at 12% p.a.
compounded annually. He paid only half of the principal after
2 years and the remaining principal and interest at the same
rate but compounded semi-annually after next two years.
How much interest was paid in those 4 years? ​

Answer 1

Answer:

The total interest paid in 4 years is Rs 4651.8

Step-by-step explanation:

Given as :

Principal borrowed = Rs 18,000

The time period for amount borrowed = 2 years

The rate of interest = 12% compound annually

According to question

Half of principal submitted in first 2 years at 12% compounded annually

Amount = principal × $(1+\dfrac{rate}{100})^{time}$

Or, A = rs 9,000 × $(1+\dfrac{12}{100})^{2}$

or, A = Rs 9,000 × 1.2544

∴   Amount = Rs 11289.6

Interest = $I_1$ = A - p

Or,           $I_1$ = Rs 11289.6 - Rs 9000

i.e           $I_1$ = Rs 2289.6

Again

Rest , Half of principal submitted in second 2 years at 12% compounded semi - annually

Amount = principal × $(1+\dfrac{rate}{200})^{2 time}$

or, A' = p' × $(1+\dfrac{rate}{200})^{2 time}$

Or, A' = rs 9000 × $(1+\dfrac{12}{200})^{4}$

Or, A' = Rs 11362.2

Interest = $I_2$ = A' - p'

Or, $I_2$ = Rs 11362.2  - Rs 9000

i.e $I_2$  = Rs 2362.2

So, The total interest paid in 4 years = $I_1$  + $I_2$

i.e  I = Rs 2289.6 + Rs 2362.2

∴   Interest = Rs 4651.8

Hence, The total interest paid in 4 years is Rs 4651.8   Answer