Jan received $2,200 from her aunt as a birthday gift. She decided to put the money in an account to save for college. The account has a fixed interest rate of 7.7%, compounded annually. How much money will be in the account after five years?
F = P(1 + r)^t
F = final amount
P = Principal amount
r = rate (in decimals)
t = time
To calculate the amount of money that will be in the account after five years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A is the amount of money in the account after t years
P is the principal amount (the initial amount of money)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, the principal amount (P) is $2,200, the annual interest rate (r) is 7.7% (or 0.077 as a decimal), the number of times interest is compounded per year (n) is 1 (compounded annually), and the number of years (t) is 5.
Plugging in these values into the formula, we get:
A = 2200(1 + 0.077/1)^(1*5)
Simplifying the equation, we have:
A = 2200(1.077)^5
Calculating (1.077)^5, we find that it is approximately 1.464
So,
A = 2200 * 1.464
Therefore, the amount of money that will be in the account after five years is approximately $3,220.8.