Question

You invest an initial $1,000 in an account that has an annual interest rate of 2%, compounded quarterly. How much money will you have in the account after 5 years? Round your answer to the nearest whole number and include units.

the growth/decay formula A = Pe^rt

A is the final amount of money in the account after a certain amount of time and at a certain interest rate.
P is the principal amount.
e = Natural Base
r is the interest rate in decimal form.
t is the time the amount of time the money is kept in the account.

or

A = P(r)n, where n is the time increment.

/

A = P(r)^t, where t is the value for time

Answer 1

`$1104.895`

Explanation:

Number of quarters in `5` years `=5\times 4=20`

Quarterly rate of compound interest `r=2/4=0.5%`

Initial amount `P=$ 1000`

hence the total amount after `5` years

`P(1+r/100)^n`

`=1000(1+0.5/100)^20`

`=1000(1.005)^{20}`

`=$1104.895`

Answer 2

Final amount after `5` years is `$1,105`

Explanation:

Principal: `P=$1000` , rate of annual interest `r=2%`

compounded quarterly , time , `t= 5` years

`:. r= 2/(4*100)= 1/200= 0.005 , t= 5*4=20`

Final amount : `A=P(1+r)^t or A=1000(1+0.005)^20`

or `A=1000(1+0.005)^20= 1000* 1.005^20~~ 1104.90` or

Final amount after `5` years is `$1,105` [Ans]