Question

Use the appropriate compound interest formula to compute the balance in the account after the stated period of time ​$10,000 is invested for years with an APR of ​% 5 and quarterly compounding. Question content area bottom Part 1 The balance in the account after 5 years is ​$ enter your response here. ​(Round to the nearest cent as​ needed.)

Answer 1

The balance in the account after 5 years is ​$12,820.37.

Explanation:

To find the account balance after 5 years of a $10,000 investment with a 5% APR compounded quarterly, we can use the compound interest formula.

Compound Interest Formula

`\large \text{$ \sf A=P\left(1+(r)/(n)\right)^(nt) $}`

where:

• A is the account balance.
• P is the principal amount invested.
• r is the interest rate (in decimal form).
• n is the number of times interest is applied per year.
• t is the time (in years).

In this case:

• P = $10,000
• r = 5% = 0.05
• n = 4 (quarterly)
• t = 5 years

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

`\sf A=10000\left(1+(0.05)/(4)\right)^(4 * 5)`

`\sf A=10000\left(1+0.0125\right)^(20)`

`\sf A=10000\left(1.0125\right)^(20)`

`\sf A=10000\left(1.2820372...\right)`

`\sf A=12820.372317...`

`\sf A=12820.37\; (2\;d.p.)`

Therefore, the account balance after 5 years is $12,820.37 (rounded to the nearest cent).