Calculating Compound Interest for a Savings Account
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)^252
Using a calculator to compute this value:
A ≈ 5000 * (1.00791667)^252
A ≈ 5000 * 5.98472378
A ≈ 29923.619
So, the value of the account will be approximately $29,923.62 when rounded to the nearest dollar.
