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You invest an initial $500 in an account that has an annual interest rate of 2%, compounded quarterly. How much money will you have in the account after 6 years? Round your answer to the nearest whole number.

A $564
B $515
C $1493
D $804

2 Answers

6 votes

You invest an initial $500 in an account that has an annual interest rate of 2%, compounded quarterly. How much money will you have in the account after 6 years? Round your answer to the nearest whole number.

A $564 ✓

  • A = P(1+r/n)^n.t
  • A=$500(1+0.02/4)^4.6
  • A=$500(1.005)^24
  • A=$500 x 1.127
  • A=$563.5 ≈ $564

B $515

C $1493

D $804

User Dten
by
7.8k points
4 votes

Answer:

A) $564

Explanation:

To calculate how much money will be in the account after 6 years, use the compound interest formula:


\boxed{A=P\left(1+(r)/(n)\right)^(nt)}

where:

  • A = Final amount.
  • P = Principal amount.
  • r = Interest rate (in decimal form).
  • n = Number of times interest is applied per year.
  • t = Time (in years).

Given values:

  • P = $500
  • r = 2% = 0.02
  • n = 4 (quarterly)
  • t = 6 years

Substitute the given values into the formula and solve for A:


A=500\left(1+(0.02)/(4)\right)^(4 \cdot 6)


A=500\left(1+0.005\right)^(24)


A=500\left(1.005\right)^(24)


A=500\left(1.1271597762...\right)


A=563.5798881...


A=564\;\sf(nearest\;whole\;number)

Therefore, the account balance will be $564 after 6 years (rounded to the nearest whole number).

User Guy Lowe
by
7.1k points

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