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:$ 55135.978Step-by-step explanation:At most, the present value of annuity must be paid. So we must find the present value of the annuityGiven in the problem, we have:Periodic Payment = PMT = $10000Rate of interest annually = i = 6.35 %= [tex]\frac{6.35}{100}[/tex]=0.0635no. of periods= n=7So to solve this, we need to use the present value formula:Present Value = Periodic payment [tex]\frac{1-(1+rate.of.interest)^{-n} }{rate.of.interest}[/tex]Present Value = PMT [tex]\frac{1-(1+i)^{-n} }{i}[/tex]Present value = 10000[tex]\frac{1-(1+0.0635)^{-7} }{0.0635}[/tex]Present Value =10000[tex]\frac{0.35011}{0.0635}[/tex]Present Value =10000 (5.5135978)Present value= $ 55135.978Which 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.