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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%. 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
Expert Solution
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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