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

Anna will need to deposit
`\$9,050.25`

Explanation:

we know that

The compound interest formula is equal to

`A=P(1+(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+(0.05)/(12))^(12*2)`

`10,000=P(1.0042)^(24)`

`P=10,000/(1.0042)^(24)`

`P=\$9,050.25`