Question

# 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?

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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