Question

Julie deposits $5000 at a rate of 4.2% compounded quarterly. With no additional deposits or withdrawals, what is the account balance after 4 years?

Answer 1

Julie deposits $5000 at an interest rate of 4.2% compounded quarterly. After 4 years, using the compound interest formula, her account balance will be $5877.35.

Step-by-step explanation:

To calculate the account balance after 4 years when Julie deposits $5000 at a rate of 4.2% compounded quarterly, you use the compound interest formula

The formula for compound interest is A = P(1 + r/n)^(nt), where:

• P is the principal amount (the initial amount of money)
• r is the annual interest rate (decimal)
• n is the number of times interest is compounded per year
• t is the number of years the money is invested for

Since the interest is compounded quarterly, n is 4. The interest rate as a decimal is 0.042 and t is 4 years.

Therefore, the formula for Julie's investment is:
A = 5000(1 + 0.042/4)^(4*4)

This simplifies to:
A = 5000(1 + 0.0105)^(16)

A = 5000(1.0105)^16

A = 5000*1.17547

Thus, Julie will have $5877.35 in her account after 4 years.

Answer 2

$5,909.50

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 4.2/100

r = 0.042 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 5,000.00(1 + 0.042/4)(4)(4)

A = 5,000.00(1 + 0.0105)(16)

A = $5,909.50

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 4.2% per year compounded 4 times per year over 4 years is $5,909.50.