Question

Anna wants to buy a car in two years and wants to have $10,000 for the purchase. How much will Anna need to deposit today in an account that earns 5% interest per year, compounded monthly?
Anna will need ____ to deposit $.

Answer 1

Answer:

Anna will need to deposit $\ 9,050.25$

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  

$t=2\ years\\A=\ 10,000\\ r=0.05\\n=12$  

substitute in the formula above  and solve for P

$10,000=P(1+\frac{0.05}{12})^{12*2}$  

$10,000=P(1.0042)^{24}$  

$P=10,000/(1.0042)^{24}$    

$P=\ 9,050.25$