Question

You have a loan outstanding. It requires making eight annual payments of $1,000 each at the end of the next eight years. 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 eight years. If the interest rate on the loan is 1%​, what final payment will the bank require you to make so that it is indifferent to the two forms of​ payment?

Answer 1

PV of 1st year end installment=990.099 (i.e.1000/(1.01^{^1})

PV of 2nd year end installment=980.296 (i.e.1000/(1.01^{^2})

Total of PV 1st and 2nd year end installments=1970.395

FV(value at the 8th year end) of the total of pv of these two installments=2133.656 1970.395(1.01^{^8})

Hence in lieu of first two installments, he will need to pay 2133.656 at the end of 8th year together with 8th years's installment.

Total amount to be paid at the 8th year end=3133.656 (i.e.2133.656+1000)

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answered by: anonymous