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A loan of $60,000 is due 10 years from today. The borrower wants to make annual...

A loan of $60,000 is due 10 years from today. The borrower wants to make annual payments at the end of each year into a sinking fund that will earn compound interest at an annual rate of 10 percent. What will the annual payments have to be?

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Answer #1

Annual cash deposit can be computed using Formula for FV of annuity as:

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

P = FV/ [(1+r) n/r]

FV = Future value of annuity = $ 60,000

P = Periodic cash deposit

r = Periodic interest rate = 0.1

n = Number of periods = 10

P = $ 60,000/ [(1+0.1)10 - 1/0.1]

   = $ 60,000/ [(1.1)10- 1/0.1]

= $ 60,000/ [(2.5937424601 – 1)/0.1]

= $ 60,000/ (1.5937424601 /0.1)

= $ 60,000/15.937424601

= $ 3,764.72369295069 or $ 3,764.72

Annual payment will have to be $ 3,764.72

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