Question

1. Find the present value of the following annuity due: $375 per month, for ten years, at 9 percent simple rate. Make sure to show your work

A. Find the future value of the following annuity: $375 per month, for fifteen years, at 8 percent simple rate.

Answer 1

In this case, compounded is happening monthly, so rate will be divided by 12 (Number of months in a year) and year is multiplied by 12.

r = 9%/12 = 0.75%

n = 10 *12 = 120

We should now calculate PVIF (Present value interest factor)

PVIF = 1 - (1+r)^-n / r

= 1 - (1+ 0.0075)^-120 / 0.0075

= 1 - (1.0075)^-120 / 0.0075

= 1 - 0.4079 / 0.0075

= 0.5921 / 0.0075

= 78.95 approx.

Present value = 375 * 78.95 = $ 29,606.25

Similarly, we have to find PVIF for the second part:

n = 15 * 12= 180

r = 8%/12 = 0.67%

PVIF = 1 - (1+r)^-n / r

= 1 - (1+ 0.0067)^-180 / 0.0067

= 1 - (1.0067)^-180 / 0.0067

= 1 - 0.3006 / 0.0067

= 0.6994 / 0.0067

= 104.39 approx.

Present value = 375 * 104.39 = $ 39,146.25