Jasmine puts $500.00 into an account to use for school expenses. The account earns 7% interest, compounded annually. How much will be in the account after 10 years?Use the formula A=P1+rnnt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.Round your answer to the nearest cent.
Question
Jasmine puts $500.00 into an account to use for school expenses. The account earns 7% interest, compounded annually. How much will be in the account after 10 years?Use the formula A=P1+rnnt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.Round your answer to the nearest cent.
Solution
To solve this problem, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
In this case:
- P = $500.00
- r = 7% = 0.07 (as a decimal)
- n = 1 (since the interest is compounded annually)
- t = 10 years
Substituting these values into the formula, we get:
A = 500(1 + 0.07/1)^(1*10) A = 500(1 + 0.07)^10 A = 500(1.07)^10
Now, calculate the value inside the brackets first:
1.07^10 = 1.967151
Then multiply this by the principal amount:
A = 500 * 1.967151 = $983.58 (rounded to the nearest cent)
So, after 10 years, Jasmine will have $983.58 in her account.
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