Anne Geyer buys some land in Utah. She agrees to pay the seller a lump sum of $6

Question

Anne Geyer buys some land in Utah. She agrees to pay the seller a lump sum of $68,000 in five years. Until then, she will make monthly simple interest payments to the seller at 12%interest.

(a) Find the amount of each interest payment. (Round the answer to the nearest cent.)
$  

(b) Anne sets up a sinking fund to save the $68,000. Find the size of her semiannual payments if her payments are due at the end of every six-month period and her money earns 8.875% interest. (Round the answer to the nearest cent.)
$  

(c) Fill in the table showing the amount in the sinking fund after each deposit. (Round the answers to the nearest cent.)

Period Starting Balance Interest Deposit Ending Balance 1 $ 0 $ 0 $ $ 2 $ $ $ $ 3 $ $ $ $ 4 $ $ $ $ 5 $ $ $ $ 6 $ $ $ $ 7 $ $ $ $ 8 $ $ $ $ 9 $ $ $ $ 10 $ $ $ $

Explanation / Answer

(a) the simple interest formula to find out the total amount of interest that she will by directly to the seller.

I =68000 * 0.12 * 5 = 40800

divide the total interest by 60 installments to determine the amount of each monthly payment.

Monthly Payment = 40800/(12 * 5) = 680

(b) For this problem, we use the future value of an ordinary annuity formula. The future value of the fund is $68000. The periodic interest rate is 0.0875/2.

The total number of monthly payments is 5*2 = 10.

Let the amount of semiannual payments are X

68000 = X [ (1+ (0.0875/2)10 -1] / (0.0875/2)

X = 5566

(c)

Period Starting Balance Interest Deposit Ending Balance 1 $ 0 $ 0 $ 5566 $ 5809.51 2 $ 5809.51 $ 243.51 $ 5566 $ 11873.18 3 $ 11873.18 $ 497.67 $ 5566 $ 18213.04 4 $ 18213.04 $ 773.86 $ 5566 $ 24834.24 5 $ 24834.24 $ 1055.20 $ 5566 $ 31749.25 6 $ 31749.25 $ 1349.01 $ 5566 $ 38971.11 7 $ 38971.11 $ 1655.86 $ 5566 $ 46513.45 8 $ 46513.45 $ 1976.33 $ 5566 $ 54390.47 9 $ 54390.47 $ 2311.02 $ 5566 $ 62617.04 10 $ 62617.04 $ 2660..57 $ 5566 $ 68183

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