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zaharov [31]
3 years ago
12

Sam invests a sum of money in a retirement account with a fixed annual interest rate of 7%

Mathematics
1 answer:
Zolol [24]3 years ago
8 0

Answer:

The initial amount of investment was $7,822

Step-by-step explanation:

The formula for compound interest, including principal sum is:

A=P(1+\frac{r}{n})^{nt}, where

  • <em>A</em> is the future value of the investment/loan, including interest
  • <em>P</em> is the principal investment amount  
  • <em>r</em> is the annual interest rate (decimal)
  • <em>n</em> is the number of times that interest is compounded per unit t
  • <em>t</em> is the time the money is invested or borrowed for

Let us use this rule to solve the question

∵ Sam invests a sum of money in a retirement account with a fixed

   annual interest rate of 7% compounded quarterly

∴ <em>r </em>= 7% = \frac{7}{100} = 0.07

∴ <em>n</em> = 4 ⇒ compounded quarterly

∵ After 13 years, the balance reaches $19,280.02

∴ <em>A</em> = 19,280.02

∴ <em>t </em>= 13

Substitute these values in the rule above to find <em>P</em>

∵ 19,280.02=P(1+\frac{0.07}{4})^{4(13)}

∴ 19,280.02=P(1.0175)^{52}

→ Divide both sides by (1.0175)^{52}

∴ 7,821.99888 = <em>P</em>

→ Round it to the nearest dollar

∴ 7,822 = <em>P</em>

∴ <em>P</em> = $7,822

∴ The initial amount of investment was $7,822.

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