orWatch a videoRhianna puts $1,000.00 into an account to use for school expenses. The account earns 5% 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
orWatch a videoRhianna puts $1,000.00 into an account to use for school expenses. The account earns 5% 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 = 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
Given: P = $1,000.00 r = 5% = 0.05 (in decimal) n = 1 (since the interest is compounded annually) t = 10 years
Substitute these values into the formula:
A = 1000(1 + 0.05/1)^(1*10) A = 1000(1 + 0.05)^10 A = 1000(1.05)^10
Now, calculate the value:
A = 1000 * 1.62889 (approximately)
A = $1,628.89
So, after 10 years, Rhianna will have approximately $1,628.89 in her account.
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