Question

Lori 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 Lori over the 10-year period is X. Calculate X.

Answer 1

$15,903

Step-by-step explanation:

Two payments are involved;

the interest payment on the loan and the payment to the sinking fund.

Annual interest payment:

= 10,000 × 9%

= $900

Payment to the sinking fund:

Amount to be accumulated by the end of the 10th year along with interest = $10,000

Amount to be deposited at the end of each year:

`=10,000* (0.08)/((1.08)^(10)-1)`

`=10,000* (0.08)/(1.158925)`

`=10,000* 0.069029`

= $690.294

Total payment per annum:

= Annual interest payment + Amount to be deposited at the end of each year

= $900 + $690.294

= $1,590.29

Total payment for the 10 year period:

= 1590.29 × 10

= $15,903