Question

1-What happens to the future value of some fixed dollar amount invested today as the interest rate decreases? Why?

2-What happens to the present value of some fixed dollar amount to be received in the future as the interest rate increases? Why?

3-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?

4-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?

5-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

As per rules I am answering the first 4 subparts of the question

1: Future value=Present value*(1+Rate)^number of periods

As the interest rate declines, the future value of a certain amount of money will also decline. This is because the compounding will happen at a lower rate.

2: Present value =Future value/(1+Rate)^number of periods

Present value is the discounted value of a future sum of money and hence if the interest rate increases, the present value will decrease.

3: as the time decreases, the present value increase. This is because discounting will be up for a lesser period of time. Also in the future amount becomes closer to the present, so its value will be higher.

4: The present value of annuity due will be higher since annuity due represents immediate payments. Payments are made at the beginning of the period and so their present value is higher. The present value of annuity is lesser since the payments are made at the end of the period.