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

$819.75

Step-by-step 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 + }(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 + }(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{ = }(1000)/(1.22) \\ P\text{ = \$819.75} \end{gathered}`

Sasha earned $819.75 doing odd jobs.