Respuesta :
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,
[tex]A[/tex] =$308, Annuity or the quarterly payment amount.
[tex]r[/tex] =1.5%, the rate of interest to be paid quarterly; thus the effective rate of interest will be: 0.375% [tex](\frac{1.5\%}{4})[/tex]
[tex]n[/tex] = 20 years, number of periodic payments, but the effective time period for the computation will be 80 payments that are: [tex](20\times4(\text{quarter}))[/tex]
[tex]\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}[/tex]
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
[tex]r[/tex] =5.5%, the coumpounded rate of interest
[tex]n[/tex] =10 years
[tex]\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}[/tex]
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:
https://brainly.com/question/14799840
