Question

Lori borrows 10,000 for 10 years at an annual e ective 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 e ective interest rate of 8%. The total payments made by Lori over the 10-year period is X: Calculate X:

Answer 1

Answer: $15,903

Step-by-step explanation:

Given that,

Lori borrows = 10,000

Time period = 10 years

Interest rate = 9%

Sinking fund (Interest rate) = 8%

Two payments are involved;

(i) the interest payment on the loan

(ii) the payment to the sinking fund

Annual interest payment = 10000 × 9%

= $900

Payment to the sinking fund:

Amount to be accumulated by the end of the 10th year along with interest = $10000

Amount to be deposited at the end of each year:

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

= $690.29

Total payment per annum = $1,590.29

Total payment for the 10 year period = 1590.29 × 10

= $15,903