Solve each exponential growth/decay problem.
5) Austin invested $11,000 in an account paying an interest rate of 5.7% compounded quarterly. Assuming no deposits or withdrawals are made, how much money would be in the account after 6 years.
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (initial investment)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
In this case:
P = $11,000
r = 5.7% = 0.057
n = 4 (quarterly compounding)
t = 6 years
Plugging in these values into the formula, we get:
A = $11,000*(1 + 0.057/4)^(4*6)
A = $11,000*(1 + 0.01425)^24
A = $11,000*(1.01425)^24
A = $11,000*(1.4150406)
A = $11,000*1.4150406
A = $15,565.45
Therefore, after 6 years, there would be approximately $15,565.45 in the account.