RS. 5000 paid is every year for ten years to pay to off a loan. What is the loan amount if interest rate be 14% per annum compounded interest.?

Question

Answer

Loan Amount Calculation with Compound Interest

Given:

Annual payment = Rs. 5000

Number of years = 10

Interest rate = 14% compounded annually

To find: Loan amount

Solution:

Let P be the principal amount

Then, the future value of the annuity is given by the formula:

FV annuity = P [(1 + r)^n - 1]/r

where r = interest rate per period and n = number of periods

Here, r = 14%/1 = 14% and n = 10

So, FV annuity = P [(1 + 0.14)^10 - 1]/0.14

Given, annual payment = Rs. 5000

So, FV annuity = 5000 [(1 + 0.14)^10 - 1]/0.14

Now, the loan amount (principal) is the present value of the future value of the annuity:

P = FV annuity / (1 + r)^n

where r = interest rate per period and n = number of periods

Here, r = 14%/1 = 14% and n = 10

So, P = [5000 [(1 + 0.14)^10 - 1]/0.14] / (1 + 0.14)^10

P = Rs. 31,359.90 (approx)

Therefore, the loan amount is Rs. 31,359.90 (approx)

Answer: The loan amount is Rs. 31,359.90 (approx) when Rs. 5000 is paid every year for ten years at an interest rate of 14% per annum compounded annually.

Answer

Ans:27263.6651153
Solution:
loan amount=
present value(annuity)[1-1/(1+i)^n]/i
5000[1-1/(1.14)^10]/0.14
=27263.6651153

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