You borrow £10,000 from a friend and agree that you will repay the loan by four equal end-of-year instalments. Your friend will charge you a constant annual interest rate of 8%. What will be your annual repayments?

Question

You borrow £10,000 from a friend and agree that you will repay the loan by four equal end-of-year instalments. Your friend will charge you a constant annual interest rate of 8%. What will be your annual repayments?

Answer 1

The amount to be repaid annually can be calculated using the formula for PV of ordinary annuity which is as follows- PV = PMT/R x (1-1/(1+R)^N)......(1)Where PMT is the periodic payment R is the interest rateN is the number of payments. Rearranging equation 1 and isolating PMT PMT = PV x R/(1-1/(1+R)^N)In the given scenario PV = £10,000R = 8%N = 4 Substituting values in equation 2 PMT =  £10,000 x 8%/(1-1/(1+8%)^4)= £800/(1-1/(1.08)^4)= £800/(1-1/(1.360489)= £800/(1- 0.735030)= £800/0.264970= £3,019.20Thus, the annual repayment amount is £3,019.20.

Question

You borrow £10,000 from a friend and agree that you will repay the loan by four equal end-of-year instalments. Your friend will charge you a constant annual interest rate of 8%. What will be your annual repayments?

Answer

Answer