Question

With the current terms, it will take another two years to repay the remaining part of your mortgage. Under the current terms, you will pay the bank € 500 a month for the next two years (a total of 24 payments), with the first of these payments taking place in a month. Now, however, you are proposing to the bank a change in the terms of the loan. You would like to repay the loan immediately for 2000 euros, and the full amount in two years. How much would you have to pay the bank after two years so that the change in terms would not matter to the bank when the interest rate on the loan is 9% per annum? (Note: answer options to the nearest thousand euros to avoid rounding errors.)

Select one:

a. Approximately EUR 10,000.

b. About 11,000 euros.

c. About 12,000 euros.

d. About 9000 euros.

Answer 1

Interest Rate	9%
Monthly Interest(9%/12)	0.0075
Before Change
Monthly Payment	500.00
Total No. of Payment	24.00
Total Payments	12000.00
Present Value of loan calculation
Present Value = A*PVF at 0.0075 r and t = 24
where A = Monthly payments, PVF = present value factor
PV of loan = 500*(1-(1+0.0075)^-24)/0.0075
= 500*21.89	10,945.00
After Change
Present Value of loan	10,945.00
LumpSumPayment	2000.00
Principal Left	8945.00
Annual Payments(A = Present Value/PVF) formula provided at last or use financial calculator)	408.65
Total Payments	9807.60
Hence, the correct option is approximately 10,000 euros

Hence, the correction option is A) Approximately EUR 10,000

The formula used is this :

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