You invest an initial $4,500 in an account that has an annual interest rate of 4.5%, compounded daily. How much money will you have in the account after 10 years? Round your answer to the nearest whole number.
amount = 4500(1 + .045/365)^3650
= 7057.21
or $ 7057 to the nearest dollar
To find out how much money you will have in the account after 10 years with compound interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (initial investment)
r is the annual interest rate (in decimal form)
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 $4,500, the annual interest rate (r) is 4.5% or 0.045 (in decimal form), the number of times interest is compounded per year (n) is 365 (daily compounding), and the number of years (t) is 10.
Substituting these values into the formula, we get:
A = 4,500(1 + 0.045/365)^(365*10)
To simplify the calculation, let's use a calculator or a spreadsheet program:
A ≈ 4,500(1 + 0.000123288)^(3650)
A ≈ 4,500(1.000123288)^(3650)
A ≈ 4,500(1.598737)
A ≈ 7,194.82
After rounding to the nearest whole number, you would have approximately $7,195 in the account after 10 years with daily compounding.