Beatrice invests her $350 at a rate of 0.25% per month compound interest.Calculate the amount Beatrice has at the end of 5 years.Give your answer correct to the nearest dollar.
Question
Beatrice invests her $350 at a rate of 0.25% per month compound interest.Calculate the amount Beatrice has at the end of 5 years.Give your answer correct to the nearest dollar.
Solution
To solve this problem, we will use the formula for compound interest, which is:
A = P (1 + r/n)^(nt)
Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
In this case, Beatrice's principal amount (P) is $350. The annual interest rate (r) is 0.25% per month, which is 3% per year in decimal form (0.03). The interest is compounded monthly, so n is 12. The time (t) is 5 years.
Substituting these values into the formula, we get:
A = 350 (1 + 0.03/12)^(12*5)
Now, calculate the expression inside the parentheses:
1 + 0.03/12 = 1.0025
Then, raise this result to the power of 60 (which is 12 times 5):
(1.0025)^60 ≈ 1.161834242728283
Finally, multiply this by the principal amount:
A = 350 * 1.161834242728283 ≈ $406.64
So, Beatrice will have approximately $407 at the end of 5 years, when rounded to the nearest dollar.
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