Question - Calculating Compound Interest for a Savings Account
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Solution:
To solve this question, we can use the compound interest formula which is: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 (decimal).n is the number of times that interest is compounded per year.t is the time the money is invested or borrowed for, in years.In this case, a grandmother deposits $5000 in an account that pays 9.5% compounded monthly, and we want to find the value of the account at the child's twenty-first birthday. Therefore, P = $5000, r = 9.5/100 = 0.095 (as a decimal), n = 12 (since interest is compounded monthly), and t = 21 years.Plugging in the values:A = 5000(1 + 0.095/12)^(12*21)A = 5000(1 + 0.00791667)^(252)A = 5000(1.00791667)^(252)Now we can calculate the value of A.A ≈ 5000(1.00791667)^252Using a calculator to compute this value:A ≈ 5000 * (1.00791667)^252A ≈ 5000 * 5.98472378A ≈ 29923.619So, the value of the account will be approximately $29,923.62 when rounded to the nearest dollar.
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