Question

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

Answer 1

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

Answer 2

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).