Question

Common information for 6 and 7

Andrew borrows 360,000 at i=.05. He repays this loan by paying off only the interest due at the end of each year to the lender and depositing a level amount Y at the end of each year into a sinking fund account offering 8% APY so as to accumulate the full balance of the loan amount in the sinking fund at the end of 20 years.

What value Y must he deposit into the SF account at the end of every year?

	A.	The answer is not listed here
	B.	10,887.33
	C.	9886.42
	D.	10,002.42
	E.	7866.80

Answer 1

According to given information Andrew barrows the amount of $360000 at 0.05 and he is paying the interest at the end of every year and the principal amount is only pending.

So for the principal repayment he is depositing the sinking fund at the end of every year which gives 8% interest per annum for repay the principal amount $360000

We can use the formula for finding the future value as below

FV = P x [ ( 1 + (r/n) )^nt-1 ] / ( r/n )

Here FV =  future value = $360000

        P = Cash flow per period  = $?

        r = rate of interest = 8% = 8/100 = 0.08

                n = compounding frequency = 1

       t = Number of years  = 20

360000= C x [ ( 1 + (0.08/1 )²⁰ – 1 ] / (0.08/1)

360000 = C X  [ ( 1 + 0.08 )²⁰ – 1 ] / (0.08)

360000 = C X ( (1.08)²⁰ -1 ) / (0.08)

360000 = C X ( 4.66095 -1 ) / (0.08)

360000 = C X (3.66095 ) / (0.08)

360000 = C X 45.761875

C = 360000 / 45.761875

C = 7866.810 ~ 7866.8

So annual payment = $7866.8