Question

American General offers a 18 year annuity with a guaranteed rate of 6.32% compounded annually. How much should you pay for one of these annuities if you want to receive payments of $1400 annually over the 18 year period?

Q: How much should a customer pay for this annuity?
A:

Answer 1

A customer should pay $12,051.28 for an 18-year annuity with annual payments of $1400 at a 6.32% guaranteed annual interest rate, calculated using the present value of an annuity formula.

Step-by-step explanation:

To determine how much a customer should pay for the annuity offered by American General, we need to use the present value of an annuity formula, which is given by PV = P × [(1 - (1 + r)^{-n}) / r], where P is the regular annuity payment, r is the interest rate per period, and n is the number of payments. Substituting the given values, we get PV = $1400 × [(1 - (1 + 0.0632)^{-18}) / 0.0632].

Carrying out the calculation:

• Calculate the discount factor: (1 + 0.0632)^{-18} ≈ 0.45583
• Subtract the discount factor from 1: 1 - 0.45583 = 0.54417
• Divide the result by the interest rate: 0.54417 / 0.0632 ≈ 8.60806
• Multiply by the payment amount: $1400 × 8.60806 ≈ $12,051.28

Therefore, the customer should pay $12,051.28 for the 18-year annuity with annual payments of $1400 at a 6.32% guaranteed annual interest rate.

Answer 2

To calculate the amount you should pay for the annuity, use the present value formula for an annuity with the given annual payments, interest rate, and number of periods.

Step-by-step explanation:

To calculate how much you should pay for the annuity, you can use the formula for the present value of an annuity. The present value of an annuity is the current worth of a series of future cash flows. In this case, the future cash flows are the annual payments of $1400 over 18 years. The formula for present value of an annuity is:

PV = PMT x ((1 - (1 + r)⁻ⁿ) / r)

In this formula, PV represents the present value, PMT represents the annual payment, r represents the interest rate per period (divided by 100 to convert it to decimal form), and n represents the number of periods. Plugging in the values from the question:

PV = $1400 x ((1 - (1 + 0.0632)^-18) / 0.0632)

Calculating this expression gives approximately:

PV ≈ $16,656.34