Question

Suppose that $2000 is invested at a rate of 4.6%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 6 years

Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

$2,631.55

Explanation:

To find the total amount in the account after 6 years, we can use the compound interest formula.

Compound Interest Formula

`\boxed{\sf 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 = $2,000
• r = 4.6% = 0.046
• n = 4 (quarterly)
• t = 6 years

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

`\implies \sf A=2000\left(1+(0.046)/(4)\right)^(4 \cdot 6)`

`\implies \sf A=2000\left(1+0.0115\right)^(24)`

`\implies \sf A=2000\left(1.0115\right)^(24)`

`\implies \sf A=2000\left(1.3157739...\right)`

`\implies \sf A=2631.54794...`

Therefore, the total amount after 6 years is $2,631.55 rounded to the nearest cent.