Question

4. A periodic deposit is made into an annuity with the given terms. Find how much should be regularly deposited in order to have the specified final amount in the account. Round your answer to the nearest dollar. Future value: $67,000 Interest rate: 2.55% Frequency weekly Time: 17 years Regular deposit amount: $

Answer 1

We are going to employ the future value formula to solve the problem.

The future value, FV, is given as:

`\begin{gathered} FV=PMT(((1+i)^n-1)/(i)) \\ FV\colon\text{Future value} \\ \text{PMT:Periodic payment} \\ i\colon\text{ Interest rate per period} \\ n\colon total\text{ number of payments} \end{gathered}`

From the question, we have the following information:

`\begin{gathered} FV\colon\text{ \$67,000} \\ i\colon\frac{2.55\text{\%}}{52}=(0.0255)/(52)=0.0004904 \\ n=52*17=884 \end{gathered}`

Thus, we have:

`\begin{gathered} 67,000=\text{PMT(}((1+0.0004904)^(884)-1))/(0.0004904)) \\ 67,000=\text{PMT(}((1.0004904)^(884)-1)/(0.0004904)) \\ 67,000=\text{PMT(}(1.5425-1)/(0.0004904)) \\ 67,000=\text{PMT(}(0.5425)/(0.0004904)) \\ 67,000=\text{PMT}(1,106.248) \\ (67,000)/(1,106.248)=\text{PMT} \\ \text{PMT}=\text{ \$60.56} \end{gathered}`

Hence, the regular deposit amount is $60.56