Question

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.

Answer 1

The amount that will be received by Terry at the end of every year for 10 years is $3,803.97

Computations:

1. First the future value will be computed:

Given,

$A$ =$308, Annuity or the quarterly payment amount.

$r$ =1.5%, the rate of interest to be paid quarterly; thus the effective rate of interest will be: 0.375% $(\frac{1.5\%}{4})$

$n$ = 20 years, number of periodic payments, but the effective time period for the computation will be 80 payments that are: $(20\times4(\text{quarter}))$

$\begin{aligned}\text{Future Value}&=\dfrac{A\times(1+r)^n-1}{r}\\&=\dfrac{\ 308\times(1+0.00375)^{80}-1}{0.00375}\\&=\ 28,672.88\end{aligned}$

2. From the determined future value that will be used in the present value formula, where 5.5% interest compounded at which Terry will receive an amount for every 10 years will be computed.

Given,

Present value =$28,672.88

$r$ =5.5%, the coumpounded rate of interest

$n$ =10 years

$\begin{aligned}\text{Present Value}&=\dfrac{A(1+r)^n-1}{r(1+r)^n}\\\ 28,672.88&=\dfrac{A(1+0.055)^{10}-1}{0.055(1+0.055)^{10}}\\A&=\dfrac{7.537}{\ 28,672.88}\\A&=\ 3,803.97\end{aligned}$

Therefore, after the payment of $308 for 20 years, Terry will start receiving the amount of $3,803.97 every 10 years.

To know more about the future value and present value, refer to the link:

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