Question

kinsey deposited money into an account in which interest is compounded monthly at a rate of 3.1%. She made no other deposits of withdrawals and the total amount in her account after 5 years was $2685.08. how much did she deposit?

Answer 1

A=2,685.08÷(1+0.031÷12)^(12×5)
=2,300.00

Answer 2

She deposit $2300 (approx.)

Explanation:

Given: Rate, R = 3.1 % compounded monthly.

Time, T = 5 year

Amount, A = $ 2685.08

To find: Deposit amount i.e., Principal value ( P )

We use Compound interest Formula,

`A=P*(1+(R)/(100))^n`

where n = no of times interest is calculated during time period.

Here, n = 12 × 5 = 60 and R=
`(3.1)/(12)`

Let P be the Principal value or deposit amount.

Substituting given value of A, R and n. we get,

`2685.08=P*(1+((3.1)/(12))/(100))^(60)`

`2685.08=P*(1+(3.1)/(12*100))^(60)`

`2685.08=P*(1+\frac{3.1}1200})^(60)`

`2685.08=P*((1200+3.1)/(1200))^(60)`

`2685.08=P*((1203.1)/(1200))^(60)`

`2685.08=P*(1.0025833)^(60)`

`2685.08=P*(1.16748438)`

`P=(2685.08)/(1.16742438)`

`P=2300.00336`

P = $ 2300 (approx.)

Therefore, She deposit $2300 (approx.)