Question

American General offers a 7-year ordinary annuity with a guaranteed rate of 6.35% compounded annually. How much should you pay for one of these annuities if you want to receive payments of $10,000 annually over the 7-year period?

Answer 1

Answer:

$ 55135.978

Step-by-step explanation:

At most, the present value of annuity must be paid. So we must find the present value of the annuity

Given in the problem, we have:

Periodic Payment = PMT = $10000

Rate of interest annually = i = 6.35 %= $\frac{6.35}{100}$=0.0635

no. of periods= n=7

So to solve this, we need to use the present value formula:

Present Value = Periodic payment $\frac{1-(1+rate.of.interest)^{-n} }{rate.of.interest}$

Present Value = PMT $\frac{1-(1+i)^{-n} }{i}$

Present value = 10000$\frac{1-(1+0.0635)^{-7} }{0.0635}$

Present Value =10000$\frac{0.35011}{0.0635}$

Present Value =10000 (5.5135978)

Present value= $ 55135.978

Which is the amount that must be paid at most to get annuities such that $10,000 annually over the 7-year period are to be received.