A demand loan of $6000 is repaid by payments of $3000 after two years, $3000 after...

A demand loan of $6000 is repaid by payments of $3000 after two years, $3000 after
four years, and a final payment after seven years. Interest is 8% compounded quarterly
for the first two years, 9% compounded semi-annually for the next two years, and 9%
compounded quarterly thereafter. What is the size of the final payment?

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Expert Solution

The process for solving the question is first we need to calculate future value at the payment date and deduct payment from amount and then taking this value as present value again future value is calculated at next payment date

amount = present value *(1+rate/n)^n*years

A) fv after 2 years

= 6000*(1+0.08/4)^4*2 = 7029.95

payment is 3000

new present value at the end of 2 years is 4029.95

B) amount at end of 4 years is

= 4029.95*(1+0.09/2)^2*2 = 4805.79

less payment = 3000

present value left at the end of 4 years is 1805.79

C) final payment will be future value of 1805.79

final pay = 1805.79*(1+0.09/4)^4*3 =2358.45

so final payment is 2358.45

jeff jeffy answered 2 years ago

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