Question

You decide to put $2000 in a savings account to save for a $3000 down payment on a new car. If the account has an interest rate of 4% per year and is compounded monthly, how long does it take until you have $3000 without depositing any additional funds?

Answer 1

`t=10.2\ years`

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=?\ years\\P=\$2,000\\A=\$3,000\\ r=0.04\\n=12`

substitute in the formula above

`3,000=2,000(1+(0.04)/(12))^(12t)`

`1.5=((12.04)/(12)})^(12t)`

Applying log both sides

`log(1.5)=log[((12.04)/(12)})^(12t)]`

`log(1.5)=(12t)log((12.04)/(12))`

`t=log(1.5)/[(12)log((12.04)/(12))]`

`t=10.2\ years`