Question

A

0) Chelsea invests $4,734 in a savings
account with a fixed annual interest rate of
4.02% compounded 4 times per year.
What will the account balance be after 12
years?
A) $7,962.65 B) $8,625.82
C) $8,287.61 D) $7,650.44

Answer 1

$7650.44

Explanation:

Annual interest rate = 4.02%

but compound 4 times per year, means quarterly compound

quarterly interest rate = 4.02%/4 = 1.005%

Account balance = 4734 * (1.01005)^48 [compound 4 times a year for 12 years]

= 4734 * 1.616

= 7650.44

Answer 2

D) $7,650.44

Explanation:

Compound Interest Formula

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

where:

• A = final amount
• P = principal amount
• r = interest rate (in decimal form)
• n = number of times interest applied per time period
• t = number of time periods elapsed

Given:

• P = $4,734
• r = 4.02% = 0.0402
• n = 4 (quarterly)
• t = 12 years

Substituting the given values into the formula and solving for A:

`\large \text{$ \sf \implies 4734\left(1+(0.0402)/(4)\right)^(4 * 12) =7650.435473$}`