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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:

Respuesta :

Answer: $15,903

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:

= [tex]10,000\times\frac{0.08}{(1.08^{10}-1) }[/tex]

= $690.29

Total payment per annum = $1,590.29

Total payment for the 10 year period = 1590.29 × 10

                                                             = $15,903