Kenny will invest $16,000 in an account with an annual interest rate of 5% and the interest is compounded quarterly. How much money will be in the account in 7 years?
How will I set this up?
r = .05/4 = .0125
every quarter year multiply by 1.0125
7 years = 28 quarter years
so
16,000 * 1.0125^28
= $ 22,655.88
Well, to set it up, you'll need to remember that compound interest formula. And by "remember," I mean "Google it." But I'll humor you and explain.
The formula for compound interest is A = P(1 + r/n)^(nt), where:
A is the final amount
P is the principal amount (starting amount)
r is the annual interest rate (in decimal form)
n is the number of times that interest is compounded per year
t is the number of years
So, in your case:
P = $16,000
r = 0.05 (5% in decimal form)
n = 4 (quarterly, so 4 times a year)
t = 7 years
Now plug those values into the formula and calculate it. But don't worry, I won't leave you hanging. Let me do the math for you.
To set up this problem, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $16,000, the annual interest rate (r) is 5% (or 0.05 as a decimal), the interest is compounded quarterly (n = 4), and the investment period (t) is 7 years.
Now, we can substitute these values into the formula and calculate the future value (A).
To find the amount of money in the account after 7 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal amount (P) is $16,000, the annual interest rate (r) is 5% (or 0.05 as a decimal), the interest is compounded quarterly, so the number of times the interest is compounded per year (n) is 4, and the number of years (t) is 7.
Now, let's plug these values into the formula and calculate the final amount in the account (A):
A = 16000(1 + 0.05/4)^(4*7)
Simplifying this calculation, we get:
A = 16000(1 + 0.0125)^(28)
Now, we can simplify the equation further by calculating the value inside the parentheses:
A = 16000(1.0125)^(28)
Using a calculator or a computer, we can evaluate (1.0125)^(28) and multiply it by 16000 to find the final amount in the account after 7 years.