Mr. Smith invested $2,500 in a savings account that earned 3% interest compounded annually. He made no additional deposits or withdrawals. Write an equation that represents the amount of money he has at the end of 4 years.
y = 2500 * (1.03)^4
= $ 2813.77
To find the equation that represents the amount of money Mr. Smith has in his savings account at the end of 4 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/amount of money at the end of the time period
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $2,500 (the initial investment)
r = 3% = 0.03 (converted to decimal form)
n = 1 (compounded annually because Mr. Smith made no additional deposits or withdrawals)
t = 4 (number of years)
Substituting the given values into the formula:
A = 2500(1 + 0.03/1)^(1*4)
Simplifying further:
A = 2500(1 + 0.03)^4
So, the equation that represents the amount of money Mr. Smith has at the end of 4 years is:
A = 2500(1.03)^4