Problema Solution
Wendy puts $10,000 in her child’s education account when her child is born and another $10,000 when the child turns 9. The account pays 12.05% interest compounded monthly. If she makes no other contributions to the account, how much will there be altogether in the account when the child turns 18?
Answer provided by our tutors
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The Compound Interest Formula is
A = P * (1 + (r/n))^(nt)
P = principal amount (the initial amount you borrow or deposit)
r = annual rate of interest (as a decimal)
t = number of years the amount is deposited or borrowed for.
A = amount of money accumulated after n years, including interest.
n = number of times the interest is compounded per year
First lets calculate the money accumulated after 9 years:
A = 10,000 (1 + (0.1205/12))^(12*9)
P = $10,000
r = 12.05% = 0.1205
t = 9 years
n = 12 (each month, since there are 12 months in the year)
A = $29,420.0431 approximately
She then puts another $10,000 so the new principal amount will be P = 29,420.0431 + 10,000 = $29,420.0431.
Again lets use the formula A = P * (1 + (r/n))^(nt) where
P = $29,420.0431
r = 12.05% = 0.1205
t = 18 - 9 = 9 years
n = 12 (each month, since there are 12 months in the year)
A = 29,420.0431 (1 + (0.1205/12))^(12*9)
A = $86,553.8935 approximately
There will be $86,553.8935 approximately when the child turns 18.