Question

1. American General offers a 18-year annuity with a guaranteed rate of 7.91​% compounded annually. How much should you pay for one of these annuities if you want to receive payments of ​$900 annually over the 18 year​ period?

2. A sailboat costs $29,546. You pay 20% down and amortize the rest with equal monthly payments over a 11​-year period. If you must pay 6.6% compounded​ monthly, what is your monthly​ payment? How much interest will you​ pay?

Answer 1

SOLUTION-1)

According to the question the american general offers an annuity for 18 years,

At the rate = 7.91% = 0.0791 compounded annually

The payment received per period = $ 900.

Using the formula

Here,  is the rate per period is the present value of all the payments.

is the payment for each period, is the rate per period and  is the number of periods.

Here, = $ 900,

= 0.0791,

= 18

= ?

Substituting the given values in the formula we get,

The payment to get the annually is = $ 8487.98