Question

Rhonda, a 40-year-old woman, is trying to determine whether she should buy a $250,000 whole

life ($3008/year) or a 20-year term life policy ($185/year). She has been told that the whole life policy will earn 1.75%
interest compounded annually on her yearly premium. She has also found that if she invested
the difference in her policy premiums in a mutual fund she could be earning a 3.75% interest rate
compounded annually. At the end of 20 years which is the better value and by what amount?

Answer 1

Explanation:

To determine which option is the better value, we need to compare the accumulated value of the two policies at the end of 20 years.

Let's start by calculating the accumulated value of the whole life policy after 20 years. The yearly premium for the whole life policy is $3008, and it earns 1.75% interest compounded annually. The formula for compound interest is:

A = P(1 + r/n)^(nt)

Where:

A = Accumulated value

P = Principal (yearly premium)

r = Annual interest rate (in decimal form)

n = Number of times interest is compounded per year

t = Number of years

For the whole life policy:

P = $3008

r = 1.75% = 0.0175 (annual interest rate)

n = 1 (compounded annually)

t = 20 (number of years)

A = $3008(1 + 0.0175/1)^(1*20)

A ≈ $3008(1.0175)^20

A ≈ $3008(1.39885)

A ≈ $4205.61

After 20 years, the accumulated value of the whole life policy is approximately $4205.61.

Now, let's calculate the accumulated value of the term life policy with the difference invested in a mutual fund. The yearly premium for the term life policy is $185, and the difference in premiums is $3008 - $185 = $2823. This difference will be invested in a mutual fund with a 3.75% interest rate compounded annually.

Using the same compound interest formula:

P = $2823

r = 3.75% = 0.0375 (annual interest rate)

n = 1 (compounded annually)

t = 20 (number of years)

A = $2823(1 + 0.0375/1)^(1*20)

A ≈ $2823(1.0375)^20

A ≈ $2823(1.91446)

A ≈ $5403.61

After 20 years, the accumulated value of the term life policy with the difference invested in a mutual fund is approximately $5403.61.

Comparing the two accumulated values, we can see that the term life policy with the mutual fund investment is the better value. The difference in accumulated values is $5403.61 - $4205.61 = $1198.

Therefore, the term life policy with the mutual fund investment is better by approximately $1198 at the end of 20 years.