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?

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Answer 1

1. If the interest rate decreases, the future value also decreases due to compounding factors reduces. (1+i)^n

i=interest rate.

2. The present value decreases if interest rate increases due to reduction in the discounting factor. 1/(1+i)^n

3. The present value increases if the time to receive the money reduces becuase of lower discounting factor.

Present value=Future value/(1+i)^n

n=number of years, if these low, the denominator will be low thus increaaasing the present value

4. Ordinary annuity:payments made at the end of the year

Annuity due:payments made at the begining of the year.

The payment made on annuity due, have a higher present value than the regular annuity. This is because of the principle of time value of money, i.e. the value of one rupee, today is greater than the value of one rupee, after one year.

5. The annuity due will have higher future value because the value will be higher for the payments that made at the begining of the period rather than end of the year.