Suppose 48,000 is invested at an interest rate of 4.2%, compounded quarterly. What will the account be in 10 years?

what is

48000( 1.0105)^40 ?

To find the future value of the investment, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:
A = the future value of the investment
P = the principal amount ($48,000 in this case)
r = the interest rate per period (4.2% = 0.042)
n = the number of compounding periods per year (4 in this case, since it's compounded quarterly)
t = the number of years (10 in this case)

Plugging in the values, we get:

A = 48,000 * (1 + 0.042/4)^(4*10)
A = 48,000 * (1 + 0.0105)^(40)
A ≈ 48,000 * (1.0105)^(40)

To calculate this, you can use a calculator or a spreadsheet.

Using a calculator, we get:

A ≈ 48,000 * 1.519545868 ≈ $72,868.21

Therefore, the account will be approximately $72,868.21 after 10 years.