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Savatey [412]
3 years ago
12

wyatt opend a savings account 4 years ago. the account earns 4%interest compounded quarterly if the current balance is $1,000.00

how much did he deposit initially round your answer to the nearest cent ​
Mathematics
1 answer:
Doss [256]3 years ago
4 0

Answer:

He deposited initially $852.82

Step-by-step explanation:

The rule of the compound interest is A=P(1+\frac{r}{n})^{nt}, where

  • A is the new amount
  • P is the initial amount
  • r is the rate in decimal
  • n is the period of the time
  • t is 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 = P(1+\frac{0.04}{4})^{4(4)}

∴ 1,000 = P(1+0.01)^{16}

∴ 1,000 = P(1.01)^{16}

→ Divide both sides by  (1.01)^{16}

∴ 852.8212622 = P

→ Round it to the nearest cent (2d.p)

∴ P = 852.82

∴ He deposited initially $852.82

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