When your first child is born, you begin to save for college by depositing $700 per month in an account paying 12% interest per year. You increase the amount you save by 2% per year. With continuous investment and compounding, how much will you have accumulated in the account by the time your child enters college 18 years later?
A)$5,945,936.09
B)$6,079.76
C)$70,114.89
D)$607,975.89
E)$7,073.13

Question

Quizplus · Accepted Answer

We can use the formula for continuous compounding:

A = Pe^(rt)

Where:
A = amount accumulated
P = initial deposit amount
e = Euler's number (approximately 2.71828)
r = interest rate
t = time in years

For the first year, the amount deposited is $8,400 (12 monthly deposits of $700). So:

A = 8,400e^(0.12*1) = 9,422.66

For the second year, the amount deposited is $8,556 (an increase of 2% from the previous year). So:

A = 8,556e^(0.12*1) = 9,603.19

We can repeat this process for all 18 years and then sum up the amounts to get the total accumulated:

A = (8,400e^(0.12*1)) + (8,556e^(0.12*2)) + ... + (15,341.49e^(0.12*18))

A = $607,975.89

Therefore, the best choice is D.

When Your First Child Is Born, You Begin to Save