how much should you deposit at the end of each month into an investment account that pays 6.5% compounded…
how much should you deposit at the end of each month into an investment account that pays 6.5% compounded monthly to have $5 million when you retire in 38 years? how much of the $5 million comes from interest? click the icon to view some finance formulas. in order to have $5 million in 38 years, you should deposit $ each month. (round up to the nearest dollar.)
Answer
Explanation:
Step1: Identify the compound - interest formula for an ordinary annuity
The formula for the future value of an ordinary annuity is $F = A\times\frac{(1 + r)^{n}-1}{r}$, where $F$ is the future value of the annuity, $A$ is the amount of each payment, $r$ is the interest rate per period, and $n$ is the number of periods. The annual interest rate $i = 6.5%=0.065$. The interest rate per month $r=\frac{0.065}{12}$. The number of years $t = 38$ years, and the number of months $n=38\times12 = 456$ months. The future value $F = 5000000$.
Step2: Rearrange the formula to solve for $A$
Starting with $F = A\times\frac{(1 + r)^{n}-1}{r}$, we can solve for $A$: [A=\frac{F\times r}{(1 + r)^{n}-1}] Substitute $F = 5000000$, $r=\frac{0.065}{12}$, and $n = 456$ into the formula. First, calculate $(1 + r)^{n}=(1+\frac{0.065}{12})^{456}$. Let $x=\frac{0.065}{12}\approx0.0054167$. Then $(1 + x)^{456}\approx1.0054167^{456}\approx11.1777$. [(1 + r)^{n}-1\approx11.1777 - 1=10.1777] $F\times r=5000000\times\frac{0.065}{12}\approx27083.33$. [A=\frac{27083.33}{10.1777}\approx2661]
Answer:
$2661$