Question

Sasha earned some money doing odd jobs last summer and put it in a savings account that earns 5% interest compounded quarterly. After 4 years, there is 1,000.00 in the account. How much did Sasha earn doing odd jobs ?

Answer 1

ANSWER

$819.75

EXPLANATION

The amount that she earned doing odd jobs (which she put in the savings acount) is called the Principal.

The savings was compounded monthly at a rate, R, of 5% for 4 years and the amount in the account is $1,000.

The formula for quarterly compounded amount is:

$A\text{ = P(1 + }\frac{R}{4})^{4t}$

where A = final amount of savings = $1000

P = prinicipal

R = rate = 5% = 0.05

t = number of years = 4

We need to solve for P. We have that:

$\begin{gathered} 1000\text{ = P(1 + }\frac{0.05}{4})^{4\cdot\text{ 4}} \\ 1000\text{ = P(1 + }0.0125)^{16} \\ 1000=P(1.0125)^{16}\text{ = P }\cdot\text{ 1.22} \\ \text{Divide both sides by 1.22:} \\ P\text{ = }\frac{1000}{1.22} \\ P\text{ = \ 819.75} \end{gathered}$

Sasha earned $819.75 doing odd jobs.