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

compounded quarterly. After 13 years, the balance reaches $19,280.02. What was the amount of
the initial investment? ROUND YOUR ANSWER TO THE NEAREST DOLLAR (do NOT put a dollar
sign $ in your answer)

1 Answer

4 votes

Answer:

The initial amount of investment was $7,822

Explanation:

The formula for compound interest, including principal sum is:


A=P(1+(r)/(n))^(nt), where

  • A is the future value of the investment/loan, including interest
  • P is the principal investment amount
  • r is the annual interest rate (decimal)
  • n is the number of times that interest is compounded per unit t
  • t 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

r = 7% =
(7)/(100) = 0.07

n = 4 ⇒ compounded quarterly

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

A = 19,280.02

t = 13

Substitute these values in the rule above to find P


19,280.02=P(1+(0.07)/(4))^(4(13))


19,280.02=P(1.0175)^(52)

→ Divide both sides by
(1.0175)^(52)

∴ 7,821.99888 = P

→ Round it to the nearest dollar

∴ 7,822 = P

P = $7,822

The initial amount of investment was $7,822.

User Xamantra
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