Question

what is the present value of an annuity that pays $680 per year for 13 years given an interest rate of 4.35% p.a.?

Answer 1

Here, the payments will be same every year, so it is an annuity. For calculating the present value of annuity, we will use the following formula:

PVA = P * (1 - (1 + r)^-n / r)          

where, PVA = Present value of annuity, P is the periodical amount = $680, r is the rate of interest =4.35% and n is the time period = 13

Now, putting these values in the above formula, we get,

PVA = $680 * (1 - (1 + 4.35%)^-13 / 4.35%)

PVA = $680 * (1 - ( 1+ 0.0435)^-13 / 0.0435)

PVA = $680 * (1 - ( 1.0435)^-13 / 0.0435)

PVA = $680 * (1 - 0.57490767404) / 0.0435)

PVA = $680 * (0.42509232595 / 0.0435)

PVA = $680 * 9.77223737829

PVA = $6645.12

So, required present value is $6645.12.