Question

As settlement of a 100,000 death benefit, a beneficiary elected to take an annuity-immediate payable monthly for 25 years. The monthly payment was calculated using an effective annual interest rate of 3 percent. After making payments for 10 years, the insurance company decided to increase the monthly payments for the remaining 15 years by changing the effective annual interest rate to 5 percent. Calculate the increase in the monthly payment.

Answer 1

Increase in monthly payment = 66

Step-by-step explanation:

Given:

Amount = 100,000

Time, n = 25 years

Rate of 3% was used for the first 10 years.

Rate of 5% was used for the remaining 15 years.

Required:

Calculate the increase in the monthly payment.

To find the increase we are to subtract the original monthly payment from the new monthly payment.

First find the original monthly payment:

Original monthly payment
`= 100000* ((1+0.03)^(^1^/^1^2^)-1))/((1-1/(1+((1+0.03)^(^1^/^1^2^)-1))^(^1^2^*^2^5^))) = 472.108741438514`

Therefore, original monthly payment % 472.109

Now calculate the new monthly payment:

New monthly payment
`= 472.108741438514 / [((1+0.03)^(^1^/^1^2^)-1)* (1-1/(1+((1+0.03)^(^1^/^1^2^)-1)^(^1^2^*^1^5^))*((1+0.05)^(^1^/^1^2^)-1)/(1-1/(1+((1+0.05)^(^1^/^1^2^)-1))^(^1^2^*^1^5^))] = 538.1868715`

New monthly payment = 538.187

Increase in monthly payment = 538.187 - 472.109 = 66.078

Increase in monthly payment ≈ 66