Question

Jenny takes out a 10-year loan of 100,000 at an annual effective rate of 8%. At the end of each year Jenny makes interest payments to the lender and sinking fund deposits into a sinking fund earning 6% annual effective. Jenny's first sinking fund deposit is $1000 and the remaining deposits are level. a) Find the total (net) interest paid on the loan. b) How would the total (net) interest paid on the loan change if the interest rate on the sinking fund increased? (Do not calculate just describe the impact):

No excel solution please

Answer 1

a)

Considering 8% interest rate for loan and assuming jenny makes 10 year interest payment.

Per year interest alone costs $ 8000. If there is no sinking fund Jenny has to make $ 8000* 10 (year) = $ 80,000.

But here jenny Depositing $1000 each year to get 6% interest which she used for interest payment, so first year she makes

payment of $ 7940, $ 7880 (2nd year), $ 7820 etc. That means each year interest payable reduced by $ 60 as she deposting $ 1000 each year.

Please see the below table to understand more.

	Amount of Loan	Interest Rate	Interest amount	Sinking Fund Deposit	Return	Cumulative Balance	Interest Earned	Interest paid
Year 1	100,000.00	8%	8,000.00	1,000.00	6%	1,000.00	60.00	7,940.00
Year 2			8,000.00	1,000.00		2,000.00	120.00	7,880.00
Year 3			8,000.00	1,000.00		3,000.00	180.00	7,820.00
Year 4			8,000.00	1,000.00		4,000.00	240.00	7,760.00
Year 5			8,000.00	1,000.00		5,000.00	300.00	7,700.00
Year 6			8,000.00	1,000.00		6,000.00	360.00	7,640.00
Year 7			8,000.00	1,000.00		7,000.00	420.00	7,580.00
Year 8			8,000.00	1,000.00		8,000.00	480.00	7,520.00
Year 9			8,000.00	1,000.00		9,000.00	540.00	7,460.00
Year 10			8,000.00	1,000.00		10,000.00	600.00	7,400.00
								76,700.00

total interest paid is $76,700 for 10 years.

b)

If there is a increase in sinking fund interest leads to decrease in interest payable to loan. Assuming 6% changed to 7% then interest earned will be increased to

$70 from $ 60 followed by interest payable reduced by $7930 from $ 7940.