Question

(20 points) You borrow $3000 for four years at an annual effective interest rate of i. The investor pays interest only on the loan at the end of each year and accumulates the amount necessary to repay the principal at the end of four years by making level payments at the end of each year into a sinking fund (an account used to accumulate money needed to pay back a debt). The sinking fund earns an annual effective interest rate of 7.5%. The total annual payment, including both interest on the loan and sinking fund deposit, is $990. Compute i.

Answer 1

Fund payment per year FVA: ([(1+r)^n-1)=r) Here, 7.5% 4 A Interest rate per annum B Number of years C Number of payments per per annum A:C Interest rate per period (r) BxC Number of periods (n) Future value of annuity (FVA) 1 7.5% 4 3,000 Fund payment per year 670.70 3000:(((1+7.5%)^4-1):7.5%) Interest rate, i 10.64% =(990-670.7)/3000

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