Question

1) You plan to contribute $2,000 to your account at the beginning of each of the next 5 years. Alternative investments of the same risk yield 3% return per year. What is the amount in your account at the end of the fifth year?

2) Find the amount today equivalent to 3 payments of $670 each with an interest rate of 2%. Payments are made at the end of each year.

3) Why is the present value of annuity due always higher than the present value of the ordinary annuity with the same inputs?

Please show all work thanks! for all three

Answer 1

1) Periodic Payment = 2000
Number of years = 5
Rate = 3%
FV using annuity due formula = (1+3%)*2000*((1+3%)⁵-1)/3% = 10,936.82

2) Periodic Payment = 670
Number of years = 3
Rate = 2%
PV using annuity formula = 670*(1-(1+2%)^-3)/2% = 1932.20

3) PV of annuity due are higher because they are paid at the beginning of period and mathematically there is factor of (1+r) multiplied to normal annuity for finding annuity due.

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