Answer:
He deposited initially $852.82
Step-by-step explanation:
The rule of the compound interest is [tex]A=P(1+\frac{r}{n})^{nt}[/tex], where
- n is the period of the time
∵ Wyatt opened a savings account 4 years ago
∴ t = 4
∵ The account earns 4% interest compounded quarterly
∴ r = 4% = 4 ÷ 100 = 0.04
∴ n = 4 ⇒ compounded quarterly
∵ The current balance is $1,000.00
∴ A = 1,000
→ Substitute these values in the rule above to find P
∵ 1,000 = [tex]P(1+\frac{0.04}{4})^{4(4)}[/tex]
∴ 1,000 = [tex]P(1+0.01)^{16}[/tex]
∴ 1,000 = [tex]P(1.01)^{16}[/tex]
→ Divide both sides by [tex](1.01)^{16}[/tex]
∴ 852.8212622 = P
→ Round it to the nearest cent (2d.p)
∴ P = 852.82
∴ He deposited initially $852.82
