91.6k views
5 votes
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?

User Trish
by
8.3k points

1 Answer

3 votes

Answer:

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.

User Jhovana
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.