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Homework answers / question archive / Kate borrows 10,000 for 10 years at an annual effective interest rate of 9%

Kate borrows 10,000 for 10 years at an annual effective interest rate of 9%

Finance

Kate borrows 10,000 for 10 years at an annual effective interest rate of 9%. At the end of each year, she pays the interest on the loan and deposits the level amount necessary to repay the principal to a sinking fund earning an annual effective interest rate of 8%. The total payments made by Kate over the 10-year period is X . Calculate X. 
A 34,905 
B 23,902 C 15,903 
 

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First we calculate Annual Payment:

Future Value = Annual Payment*((1+r)^n - 1/r)

$10,000 = Annual Payment * (((1+8%)^10 - 1)/8%)

$10,000/ (((1+8%)^10 - 1)/8%) = Annual Payment 

$10,000/14.4866 = Annual Payment

Annual Payment = $690.295

 

Now We calculate Total Payment:

Total Payment = Number of Payments * (Sinking Fund Payment + Interest Payment)

= 10*($690.295+($10,000*9%))

= 10*$1,590.295

Total Payment = $15,902.95

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