Question

You have a loan outstanding. It requires making three annual payments at the end of the next three years of $2000 each. Your bank has offered to allow you to skip making the next two payments in lieu of making one large payment at the end of the loan's term in three years. If the interest rate on the loan is 6%, what final payment will the bank require you to make so that it is indifferent between the two forms of payment?

Answer 1

The future value of annual three payments at the end of 3rd year will be the final payment that bank requires
so that it is indifferent between two forms of payment.
By using Future value of annuity formula we can calculate this final payment.
Future value of annuity = P*{[(1+r)^n - 1]/r}
Future value of annuity = final payment that bank requires = ?
P = annual loan payment = $2000
r = interest rate on loan = 6%
n = number of years = 3
Future value of annuity = 2000*{[(1+0.06)^3 - 1]/0.06}
Future value of annuity = 2000*3.1836
Future value of annuity = 6367.20
The final payment of $6367.20 that bank requires you to make so that it is indifferent
between two forms of payment.