Question

James wants to be able to make a $30,000 down payment on a new home in three years. If he can invest his savings in an account that earns 6% interest per year, compounded monthly, about how much will James need to deposit today to achieve his goal?

A.
$25,002
B.
$25,069
C.
$25,189
D.
$35,730

Answer 1

James needs to deposit $25,069 (B) to achieve his goal

Step-by-step explanation:

The formula to apply is :

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

where;

A=Amount at the end of the period=$30,000

P=amount invested at the beginning=?

r=rate of interest=6%=0.06

n=number of compounding per year=12

t=time for the invested money to mature=3

Applying the formula to get P

$A=P(1+r/n)^{nt} \\\\\\30,000=P(1+\frac{0.06}{12} )^{12*3} \\\\\\30,000=P(1+0.005)^{36} \\\\30,000=P(1.005)^{36} \\\\\\30,000=P(1.19668)\\\\\\30,000/1.19668=P\\\\\\25069.35=P$

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