Question

An annuity that pays $14,000 a year at an annual interest rate of 5.04 percent costs

$145,000 today. What is the length of the annuity time period?

Answer 1

To determine the length of the annuity time period, we will use the Present Value of Annuity (PVA) formula:

PVA = PMT × (1 - (1 + r)^(-n)) / r

Where:

- PVA is the present value of the annuity, which is $145,000 in this case.

- PMT is the annual payment, which is $14,000.

- r is the annual interest rate, which is 5.04% or 0.0504 as a decimal.

- n is the number of years or length of the annuity time period, which we need to find.

First, let's rearrange the formula to solve for n:

n = -log(1 - (PVA × r) / PMT) / log(1 + r)

Now, we can plug in the given values:

n = -log(1 - ($145,000 × 0.0504) / $14,000) / log(1 + 0.0504)

n ≈ 13.96

Since the annuity time period must be a whole number, we can round up to get the nearest whole number:

n ≈ 14

The length of the annuity time period is approximately 14 years.