Basic loan calculation word problem

**Deutz** · February 24th 2010, 01:48 AM

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

**Soroban** · February 24th 2010, 07:32 AM

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

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

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

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

**Wilmer** · February 24th 2010, 07:53 AM

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

**Deutz** · February 24th 2010, 06:12 PM

Thank you both for your replies. Much appreciated!

Thread: Basic loan calculation word problem

LinkBack

Thread Tools

Display

Basic loan calculation word problem

Thanks

Similar Math Help Forum Discussions

[SOLVED] Basic Trig Word Problem

Interest/Loan Payment Word Problem

Basic word problem

Word Problem Very Basic

grade calculation word problem

Search Tags