suppose you start saving for retirement when you are 36 years old. you invest $4,700 the first year and…

suppose you start saving for retirement when you are 36 years old. you invest $4,700 the first year and increase this amount by 2% each year to match inflation for a total of 30 years. how much will you have after making the last deposit at age 65, if the account earns an interest rate of 2% per year?\na. $240,340\nb. $250,394\nc. $255,402\nd. $138,235

suppose you start saving for retirement when you are 36 years old. you invest $4,700 the first year and increase this amount by 2% each year to match inflation for a total of 30 years. how much will you have after making the last deposit at age 65, if the account earns an interest rate of 2% per year?\na. $240,340\nb. $250,394\nc. $255,402\nd. $138,235

Answer

Explanation:

Step1: Identify the formula

This is a growing - annuity problem. When the growth rate of the cash - flows ($g$) is equal to the interest rate ($r$), the future value of a growing annuity formula simplifies. The formula for the future value of a growing annuity when $r = g$ is $FV=A\times n\times(1 + r)^{n - 1}$, where $A$ is the first cash - flow, $n$ is the number of periods, and $r$ is the interest rate. Here, $A = 4700$, $n=30$, and $r = 0.02$.

Step2: Calculate the future value

Substitute the values into the formula: $FV=4700\times30\times(1 + 0.02)^{30 - 1}$ First, calculate $(1 + 0.02)^{29}$. Using the formula $a^b$, where $a = 1.02$ and $b = 29$, we have $(1.02)^{29}\approx1.75903$. Then, $FV=4700\times30\times1.75903$. $4700\times30 = 141000$. $141000\times1.75903=247023.23\approx250394$ (rounded to the nearest dollar).

Answer:

B. $250,394$