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.