Question

Answer the following questions: What happens to the future value of some fixed dollar amount invested today as the interest rate decreases? Why? What happens to the present value of some fixed dollar amount to be received in the future as the interest rate increases? Why? What happens to the present value of some fixed dollar amount to be received in the future as the time to receive the money decreases? Why? Which will have a higher present value, assuming the same discount rate, same # of payments, and same amount of payments, an ordinary annuity or an annuity due? Why? Which will have a higher future value, assuming the same discount rate, same # of payments, and same amount of payments, an ordinary annuity or an annuity due? Why?

Answer 1

1: Future value of a fixed dollar amount decrease with a decline in interest rates. This is because Future value = Present value*(1+rate)^n. The compounding rate decreases and so the future value reduces.

2: Present value of a fixed amount to be received in future decreases as interest rate increases. This is because the present value is computed by discounting future cash flows.

3: The present value of amount to be received in future increases as the time decreases. This is because discounting reduces. Present value = Future value/ (1+rate)^n as the value of n is lower, the present value is higher.

4: Annuity due will have a higher present value as it is received earlier than the ordinary annuity. Annuity due is received at the beginning of the period and so will be discounted lesser.

5: Annuity due will have a higher future value since it remains invested for a longer period of time.