Question

Ben makes a deposit of $1,200 into a savings account. The bank calculates simple interest annually at a rate of 6%. Interest is added every year on the anniversary of the initial deposit. How many years must Ben wait before his investment exceeds $1,500? Give your answer in years.

Answer 1

Ben must wait more than 4.2 years

Explanation:

step 1

we know that

The simple interest formula is equal to

`A=P(1+rt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

`t=?\ years\\ P=\$1,200\\r=6\%=6/100=0.06\\A>\$1,500`

substitute the values

`1,200(1+0.06t)>1,500`

Solve for t

Divide by 1,200 both sides

`(1+0.06t)>1.25`

Subtract 1 both sides

`0.06t>1.25-1`

`0.06t>0.25`

Divide by 0.06 both sides

`t>4.2\ years`

therefore

Ben must wait more than 4.2 years