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A demand loan of ​$8000.00 is repaid by payments of ​$3500.00 after two ​years, $3500.00 after...

A demand loan of ​$8000.00 is repaid by payments of ​$3500.00 after two ​years, $3500.00 after four ​years, and a final payment after eight years. Interest is 7​% compounded monthly for the first 2 ​years, 8​% compounded semi-annually for the next two ​years, and 8​% compounded quarterly thereafter. What is the size of the final​ payment?

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Answer #1

Demand Loan = $8,000.00

- First payment is repaid after two years = $3500

Interest is compounded monthly for first 2 years at 7%

Loan balance with interest after 2 years = 8000(1+0.07/12)2*12

= $ 9198.45

Loan balance after first repayment = $ 9198.45 - $3500

= $ 5,698.45

- Second payment is repaid after next two years = $3500

Interest is compounded semiannually for next 2 year at 8%

Loan balance with interest for next 2 years = $ 5698.45(1+0.08/2)2*2

= $ 6666.38

Loan balance after second repayment = $6666.38 - $3500

= $ 3,166.38

- After that Interest is compounded quarterly for last four years at 8%

Loan balance with interest for last 4 years = $ 3166.38(1+0.08/4)4*4

= $ 4346.76

So, the size of last payment is $ 4346.76

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