Question

Jane plans to retire in 30 years and would like to have $500,000 in her account. If the interest on her account is 3.92% compounded monthly, how much should she put into her account every month? A. 1,633.33 B. 1,388.89 C. 730.74 D. 653.33 Which would result in the need for a larger monthly deposit to a retirement account with the same ending balance? A. Half the number of years before the money is withdrawn from the account B. Half the interest rate

Answer 1

$A=\frac{P[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}}$

A$=$ $ 500,000

P$=?$

r$=$ $\frac{3.92}{1200}$ Compounded monthly

n$=$ 12

t$=$ 30 years

$500,000=\frac{P[(1+\frac{3.92}{1200})^{12×30}-1]}{\frac{3.92}{1200}}$

$500,000=684.24P$

$P=730.74$

Half of the years we will use 15 years:

$500,000=\frac{P[(1+\frac{3.92}{1200})^{12×15}-1]}{\frac{3.92}{1200}}$

$500,000=244.49P$

$P=2045.09$

For half the interest we use 1.96% so:

$500,000=\frac{P[(1+\frac{1.96}{1200})^{12×30}-1]}{\frac{1.96}{1200}}$

$500,000=489.50P$

P=1021.45

Half the number of years will result in a larger monthly deposit of 2045.09