Thread: Basic loan calculation word problem

1. Basic loan calculation word problem

I'm trying to help my son with his homework but this has me stumped; the answer is in the back of the book but I've no idea how to arrive at it.

For this loan: ......

principal + interest = $2835 was repaid over a Period of 15 months and pays Interest at a rate of 4% per year What was the principal of the loan? Any idea what steps you would use to solve this? Thanks in advance 2. Hello, Deutz! For this loan: Principal + Interest =$2835
was repaid after a Period of 15 months
and pays Interest at a rate of 4% per year

What was the Principal of the loan?
I assume that this is Simple Interest.

$\text{Formula: }\;A \;=\;P(1 + i)^n$

. . . $\text{where: }\:\begin{Bmatrix}P &=& \text{principal} \\ i &=& \text{annual interest rate} \\ n &=& \text{number of years} \\ A &=& \text{final amount} \end{Bmatrix}$

The number of years is: . $\text{15 months} \quad\Rightarrow\quad \frac{15}{12} \:=\:\frac{5}{4} \:=\:1.25\text{ years}$

$\text{So we have: }\:\begin{array}{ccc} A &=& 2835 \\ i &=& 0.04 \\ n &=& 1.25 \end{array}$

$\text{Substitute: }\;2835 \;=\;P(1+0.04)^{1.25} \quad\Rightarrow\quad P(1.04)^{1.25} \;=\;2835$

$\text{Therefore: }\;P \;=\;\frac{2835}{(1.04)^{1.25}} \;=\;2699.363611 \;\approx\;\269.36$

3. If TRULY simple interest (no compounding):
p + .05p = 2835.00 : 5% over 1.25 years = 4% over 1 year
p(1.05) = 2835.00
p = 2835 / 1.05 = 2700.00

4. Thanks

Thank you both for your replies. Much appreciated!