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

Answer:

$4125.

Step-by-step explanation:

When solving for the principal we still need to use the formula $A = P(1+\dfrac{r}{n})^{nt}$.

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.

$A=P(1+\dfrac{r}{n})^{nt}$

$4369.20=P(1+\dfrac{0.033}{4})^{4(1.75)}$

$4369.20=P(1+0.00825)^{7}$

$4369.20=P(1.00825)^{7}$

$4369.20=P(1.05919912849)$

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

$\dfrac{4369.20}{1.05919912849}=\dfrac{P(1.05919912849)}{1.05919912849}$

P = 4125.00339406 or $4125.

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

$A=P(1+\dfrac{r}{n})^{nt}$

$A=4125(1+\dfrac{0.033}{4})^{4(1.75)}$

$A=4125(1+0.00825)^{7}$

$A=4125(1.00825)^{7}$

$A=4125(1.05919912849)$

$A=4369.19640502$ or $4369.20$