tammy is going to invest to help with a down payment on a home. how much would she have to invest to have…

tammy is going to invest to help with a down payment on a home. how much would she have to invest to have $24,700 after 10 years, assuming an interest rate of 1.02% compounded quarterly? do not round any intermediate computations, and round your final answer to the nearest dollar. if necessary, refer to the list of financial formulas.

tammy is going to invest to help with a down payment on a home. how much would she have to invest to have $24,700 after 10 years, assuming an interest rate of 1.02% compounded quarterly? do not round any intermediate computations, and round your final answer to the nearest dollar. if necessary, refer to the list of financial formulas.

Answer

Explanation:

Step1: Identify the compound - interest formula for present value

The compound - interest formula for present value is $PV=\frac{FV}{(1 + \frac{r}{n})^{nt}}$, where $PV$ is the present value, $FV$ is the future value, $r$ is the annual interest rate (in decimal), $n$ is the number of times compounded per year, and $t$ is the number of years.

Step2: Convert the given values to the appropriate form

The annual interest rate $r = 1.02%=0.0102$, $n = 4$ (compounded quarterly), $t = 10$ years, and $FV=$24700$.

Step3: Substitute the values into the formula

First, calculate $(1+\frac{r}{n})^{nt}=(1 + \frac{0.0102}{4})^{4\times10}=(1+0.00255)^{40}$. Using a calculator, $(1 + 0.00255)^{40}\approx1.10794$. Then, $PV=\frac{24700}{(1 + 0.00255)^{40}}=\frac{24700}{1.10794}\approx22293$.

Answer:

$22293$