The amount that will be received by Terry at the end of every year for 10 years is $<u>3,803.97</u>
Computations:
1. First the future value will be computed:
Given,
=$308, Annuity or the quarterly payment amount.
=1.5%, the rate of interest to be paid quarterly; thus the effective rate of interest will be: 0.375% ![(\frac{1.5\%}{4})](https://tex.z-dn.net/?f=%28%5Cfrac%7B1.5%5C%25%7D%7B4%7D%29)
= 20 years, number of periodic payments, but the effective time period for the computation will be 80 payments that are: ![(20\times4(\text{quarter}))](https://tex.z-dn.net/?f=%2820%5Ctimes4%28%5Ctext%7Bquarter%7D%29%29)
![\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}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Ctext%7BFuture%20Value%7D%26%3D%5Cdfrac%7BA%5Ctimes%281%2Br%29%5En-1%7D%7Br%7D%5C%5C%26%3D%5Cdfrac%7B%5C%24308%5Ctimes%281%2B0.00375%29%5E%7B80%7D-1%7D%7B0.00375%7D%5C%5C%26%3D%5C%2428%2C672.88%5Cend%7Baligned%7D)
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
=5.5%, the coumpounded rate of interest
=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}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Ctext%7BPresent%20Value%7D%26%3D%5Cdfrac%7BA%281%2Br%29%5En-1%7D%7Br%281%2Br%29%5En%7D%5C%5C%5C%2428%2C672.88%26%3D%5Cdfrac%7BA%281%2B0.055%29%5E%7B10%7D-1%7D%7B0.055%281%2B0.055%29%5E%7B10%7D%7D%5C%5CA%26%3D%5Cdfrac%7B7.537%7D%7B%5C%2428%2C672.88%7D%5C%5CA%26%3D%5C%243%2C803.97%5Cend%7Baligned%7D)
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:
brainly.com/question/14799840