Question

Find the accumulated value of $4000 at the end of 5 years if the nominal rate of interest is 4% compounded quarterly for first 1.5 years, the effective (annual) rate of discount is 7% for the next 9 months, the nominal rate of discount is 6% compounded monthly for the next year, and the annual effective interest rate is 5% for the last 21 months. 1. Ir.c 1. A payment of SX three years from now along with a payment of $4X five years from now repays a debt of $50,000 at a 4% annual effective compound interest. Find SX. (Hint: the questions means that you borrow $50,000 at time zero, and then pay back SX three years from now and S4X five years from now.) 2.

Answer 1

If you have borrowed $ 50000 now at an compounding annual rate of 4%, Your liability would grow to $ 56243.2 (50000*1.04^3)

three years from now.

And we make a payment of $ X at the end of 3rd yr, then liability would reduce to $ (56243.2-X).

and would again grown to $ [(56243.2-X)*1.04^2] by the end of 5 yrs.

which would be completely repaid by $ 4X.

there by we can deduce an equation : 4X = (56243.2-X)*1.04^2.

4X = (56243.2-X)*1.0816

4X = 60832.64-1.0816X

5.0816X = 60832.64

X =$ 11,971.16