Starting at age ten, Celine's parents deposit 60 dollars each month into an account earning 4.4% APR compounded monthly. How much will she have when she turns 18?

Step-by-step solution

1. 1

   Extract the three inputs. The payment is PMT = \60$; the term runs from age$10$to age$18$, so$t = 8$ years; and compounding is monthly, so

   $i = \frac{0.044}{12} = 0.0036666667, \qquad n = 12 \times 8 = 96$

2. 2

   Choose the ordinary-annuity formula. Equal deposits at regular intervals accumulate to

   $FV = PMT \cdot \frac{(1+i)^{n} - 1}{i}$

   This assumes each deposit is made at the end of its month, the standard convention unless the problem says "beginning of each month".

3. 3

   Compute the accumulation factor to at least six decimals.

   $(1.0036666667)^{96} = 1.42099345$

   Rounding this to $1.421238$ instead — a difference in the fourth decimal — pushes the final answer about \4$ too high, which matters when the answer is required to the cent.

4. 4

   Evaluate the future value.

   $FV = 60 \times \frac{0.42099345}{0.0036666667} = 60 \times 114.816395 = \$6{,}888.98$

5. 5

   Separate principal from interest. The parents deposited 60 \times 96 = \5{,}760$, so

   $6888.98 - 5760 = \$1{,}128.98$

   came from interest — about $16.4\%$ of the balance.

6. 6

   Sanity-check the magnitude. With no interest at all the balance would be exactly \5{,}760$; with all$$5{,}760$earning the full$8$years at$4.4%$it would be$5760 \times 1.42099 = $8{,}184.90$. The true answer sits between, closer to the lower end because the average deposit has been invested for only about half the term.