Question

When Anthony was born, his mom put aside $1000 in a savings account that earns 1% interest compounded monthly. When Anthony is 18, will he have enough money to purchase a $15,000 car? If not, how much should she have deposited to be sure he has $15,000?

Answer 1

The applicable formula is;

A = P(1+r)^nt

Where
A = Accumulate amount
P = Initial invested amount
r = Annual interest rate
n = Number of  payments in a year
t = Time in years

First part of the question: Accumulated amount after 18 years
Substituting;
A = 1000(1+0.01)^12*18 = $8,578.61

Since the car costs $15,000 and the amount in the bank after 18 years is $8,578.61, Anthony wouldn't be able to afford the car.

Second part of the question: The amount which should have been deposited for Antony to afford the car after 18 years

15,000 = P (1+0.01)^12*18
15,000 = P*8.5786
P = 15,000/8.5786 = $1,748.54
Therefore, for Antony to afford the $15,000 after 18 years, the mum should have deposited $1,748.54.