Question

Meredith invested $5,500 into an account that earned 5% interest per year. When she cashed out the investment to use it as a down payment for a new car, it was worth a total of $7,739.05.

Which equation describes Meredith's investment based on t, the number of years she kept the account open?



A: t=7,739.05 (5,500)^0.05

B: 7,739.05=5,500(1.05)^t

C: t=7,739.05 (5,500)^1.05

D: 7,739.05= 5,500(0.05)^t

Answer 1

Answer: B.
`7739.05=5500(1.05)^t`

Explanation:

The formula to find the compound amount (compounded yearly):-

`A=P(1+r)^t`, where P is the principal amount invested, is the rate of interest and t is time period.

As per given , we have

P=$5500 , r=5% = 0.05 and A = $7,739.05.

Substitute all the values in the formula , we get

`7739.05=5500(1+0.05)^t`

`7739.05=5500(1.05)^t`

Hence, the equation describes Meredith's investment based on t, the number of years she kept the account open :
`7739.05=5500(1.05)^t`