For the last 20 years, terry has made regular quarterly payments in the amount of $308 into an account paying 1.5% compounded quarterly. if, at the end of the 20 year period, terry stops making deposits, transfers the balance to an account paying 5.5% interest compounded annually, and withdraws a annual salary from the account, determine the amount that he will receive every year for 10 years. round to the nearest cent.
a. $28,672.88
b. $3,803.97
c. $28,780.40
d. $3,074.66

Base on my research, Terry will receive an amount of $3,803.97 annually for 10 years. The amount that Terry will receive is affected by the amount she paid for the last 20 years with the interest and also it is affected by the 5.5% interest compounded annually.

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pamateriales pamateriales · Answer 2 · 2019-11-28T01:41:26+01:00

Answer:

The amount that he will receive every year for 10 years is b. $3,803.97

Explanation:

Hi, first we need to find out how much money he has from the previous investment, for that, we need to use the following equation.

[tex]FutureValue=\frac{A((1+r)^{n}-1) }{r }[/tex]

Where:

A= Annuity or periodic payment made (in our case, $308/quarter)

r = effective rate (in our case 1.5% / 4 = 0.375% effective quarterly)

n = Number of periodic payments (in our case, 20*4= 80 payments)

So, everything should look like this:

[tex]FutureValue=\frac{308((1+0.00375)^{80}-1) }{0.00375 }=28,672.88[/tex]

Now, the money we count with is $28,672.88, and taking into account that the rate will change to 5.5% compounded annually (which is the same as effective annually), we need to find the annual salary that Terry can withdraw from his account so it will last for exactly 10 years. For that, we need to use the following formula and solve for "A"

[tex]PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }[/tex]

In this case, r would be 0.055, n=10 and the present value is $28,672.88. Everything should look like this.

[tex]28,672.88=\frac{A((1+0.055)^{10}-1) }{0.055(1+0.055)^{10} }[/tex]

[tex]28,672.88=A(7.537625829)[/tex]

[tex]A=3,803.97[/tex]

So, the account, determine the amount that he will receive every year for 10 years is $3,803.97

Best of luck