Question

3. March deposited money into an account in which interest is compounded quarterly at a rate of 3.3%. How much did he deposit if the total amount in his account after 21 months was $4369.20, and he made no other deposits or withdrawals?

Answer 1

$4125.

Explanation:

When solving for the principal we still need to use the formula
`A = P(1+(r)/(n))^(nt)`.

Let's take all the variables that we do have available and list them out.

A = $4369.20

r = 3.3% or 0.033

n = 4 (Quarterly)

t = 21 months or 1.75 years

Now we can substitute the values and solve for the principal.

`A=P(1+(r)/(n))^(nt)`

`4369.20=P(1+(0.033)/(4))^(4(1.75))`

`4369.20=P(1+0.00825)^(7)`

`4369.20=P(1.00825)^(7)`

`4369.20=P(1.05919912849)`

Now we need to divide both sides with 1.05919912849 to get the principal.

`(4369.20)/(1.05919912849)=(P(1.05919912849))/(1.05919912849)`

P = 4125.00339406 or $4125.

To check for our answer, we can simply substitute the values including the principal and excluding the total.

`A=P(1+(r)/(n))^(nt)`

`A=4125(1+(0.033)/(4))^(4(1.75))`

`A=4125(1+0.00825)^(7)`

`A=4125(1.00825)^(7)`

`A=4125(1.05919912849)`

`A=4369.19640502` or
`4369.20`