Question

Justin opened a savings account 3 years ago the account earns 7% interest compounded quarterly if the current balance is 800.00 how much did he deposit initially

Answer 1

The initial amount he deposited is 649.67

Step-by-step explanation:

time = t = 3 years

rate = r = 7% = 0.07

n = number of times it was compounded

n = quarterly = 4

The current balance = A = 800

P = in

amount deposited

We apply the compound interest formula to get the amount deposited:

`A\text{ = P(1 +}(r)/(n))^(nt)`
`\begin{gathered} 800\text{ = P(1 +}(0.07)/(4))^(4*3) \\ 800=P(1+0.0175)^(12) \end{gathered}`
`\begin{gathered} 800=P(1.0175)^(12) \\ 800\text{ = P(1.2314)} \\ \text{divide both sides by 1.2314} \\ \frac{800}{1.2314\text{ }}=\frac{\text{P(1.2314)}}{1.2314} \\ P\text{ = 649.67} \end{gathered}`

The initial amount he deposited is 649.67