Question

How much must be deposited today into the following account in order to have $ 65,000 in 8 years for a down payment on a​ house? Assume no additional deposits are made.
An account with annual compounding and an APR of 4​%
​$
nothing should be deposited today.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Answer 1

Answer:

$\ 47,494.86$

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

$A=P(1+\frac{r}{n})^{nt}$  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

$t=8\ years\\ A=\ 65,000\\ r=4\%=4/100=0.04\\n=1$  

substitute in the formula above  

$65,000=P(1+\frac{0.04}{1})^{1*8}$  

$65,000=P(1.04)^{8}$  

Solve for P

$P=65,000/(1.04)^{8}$  

$P=\ 47,494.86$