Question

The cost of attendance at State College is $19,500 for the first year. Devise a periodic savings plan that will allow you to make small deposits for 5 years at a simple interest rate of 1.5% and save enough to pay for the first year at the college. 15 [email protected]!!

Answer 1

We are told to use simple interest rate. Formula for this is:
$A=P*(1+r*t)$

Where:
A= total accumulated amount (principal + interest)
P= principal
r= yearly percentage rate
t= number of years

We need to save $19500 for the first year at a college. This is the amount we will have at the account after five years. In our case this is A.
Principal is the amount we need to put into savings to get the total amount needed. In our case this is P.
Yearly percentage rate is the percentage by which our savings increase at the end of a year. In our case this is r.
t is number of years that we are holding our money on the bank account.

To solve this problem we will assume that we are putting same amount each month on the bank account.

We are given:
A=$19500
P=?
r=1.5%
t=5 years

First step is to transform r into decimal number:
$r= \frac{1.5}{100} =0.015$

Now we get back to our formula and we solve it for P:
$A=P*(1+r*t) \\ P= \frac{A}{1+r*t}$
We insert numbers and we get our principal:
$P= \frac{19500}{1+0.015*5} \\ P=18139.53$

We need to put $18139.53 into savings to get required amount after 5 years or 5*12=60months. Assuming that we put same amount each month into savings we need to put
$18139.53 / 60 = 302.33$

This is our solution for this problem. This is closest to the amount we would need to put in real life. In real life we would earn interest onto interest and our monthly amount would be smaller.