interest formulas

**jason03** · April 22nd 2008, 08:33 AM

I was looking for a strategy for a problem I was working on

A car may be purchased with a 3k downpayment now and 60 month payments of 280. If the interest rate is 12% compounded monthly, what is the price of the car?

I know that 12% is the nominal rate and that you have to divide 12% by 12 months to get 1% interest per month.

So do I find the effective rate and than apply that interest rate to the 5 years of payments made?

**colby2152** · April 22nd 2008, 08:37 AM

Originally Posted by jason03

A car may be purchased with a 3k downpayment now and 60 month payments of 280. If the interest rate is 12% compounded monthly, what is the price of the car?

$3000+280a_{\overline{60|}}$

That annuity is priced using 12% compounded monthly, or $1.12^{\frac{1}{12}} -1 = .009488793 \rightarrow i^{(m)}$ interest.

$a_{\overline{60|}} = \frac{1-v^{60}}{i^{(m)}}$

**jason03** · April 22nd 2008, 08:41 AM

so your saying that the interest per month over the 5 year period is just under 1%?...

Is that considering compounding?

Thanks

**Soroban** · April 22nd 2008, 01:54 PM

Hello, Jason!

We're expected to know the Amortization Formula

. . $A \;=\;P\cdot\frac{i(1+i)^n}{(1+i)^n-1} \qquad \text{where}\:\begin{Bmatrix}A &=& \text{periodic payment} \\ P &=& \text{principal borrowed} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}$

A car is purchased with a $3,000 downpayment and 60 monthly payments of $280.
If the interest rate is 12% compounded monthly, what is the price of the car?

We will use this variation: . $P \;=\;A\cdot\frac{(1+i)^n-1}{i(1+i)^n}$

We have: . $A = 280,\;i \:=\:\frac{12\%}{12} \:=\:0.01,\;n \,=\,60$

Hence: . $P \;=\;280\cdot\frac{1.01^{60} - 1}{(0.01)(1.01)^{60}} \;=\;12587.41075$

Therefore, the amount of the loan is $\$12,587.41$

. . and the price of the car is: . $\$12.587.41 + 3,000 \;=\;\$15,587.41$

**jason03** · April 22nd 2008, 07:27 PM

Thanks!,..Im studying Mechanical Engineering and am taking my first Engineering Economic Analysis Class. Im very rusty with finance and economics so thanks again.

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