Thread: Simple Interest

"The local store advertises a stereo for $1095, or $100 deposit and $32 per week for 2 years."

a) how much money does the stereo end up costing?

I have

b)what equivalent rate of simple interest is being changed over the 2 years?

simple interest, so







106.53%

In the solution manual the answer is given as 117.24%

No, no. Your method would be fine if there were no payments. You paid it all off at the end. To make it easy on yourself, try it with just two payments, one at the end of one year and the last and the end of two years. Get that and you should be able to see how to do it with 104 payments.

I don't follow, what would the repayments be if there were only 2? Wouldn't I need to know the interest rate?

Kind regards,

If you make only two payments, one at year one and the second at year two, it goes like this.

0: Original Loan Amount
1-: Add Interest on the entire amount for One Year
1+: Subtract First Payment - This leave some amount less than the entire amount.
2-: Add interest on the remaining amount
2+: Subtract the second payment and owe nothing.

Example: 1999 @ 5% Simple.

0: $1,000.00
1-: $1,000.00 + $1,000.00*0.05*1 = $1,050.00
1+: $1,050.00 - $537.81 = $512.19
2-: $512.19 + $512.19*0.05*1 = $537.80
2+: $537.80 - $537.81 = Pretty Close to Zero

What is most important to notice is that interest in the first year was much more than the interest in the second year. $50.00 vs. $25.61 The interest RATE was the same, but the principle balance changed as soon as you made a payment.

I can follow you're example but I'm not given an interest rate to begin with.

Saying x as my rate

0: $1,905.00
1-: $1,905.00 + $1,905.00*x*1 = $1,905.00(x+1)
1+: $1,905.00(x+1) - $800 one years repayments =...
2-:
2+:

Hope this is clear?

After $100 down: $995

104 @ 32 = 3328 (2 years)

3328 - 995 = 2333 ; 1 year = 2333/2 = 1166.5

1166.5 / 995 = 1.17236 = 117.24 %

Btw, you "Shylock account" will look like this:

Code:

WEEK PRICE    PAYMENT  INTEREST   BALANCE
00  1095.00   -100.00     .00     995.00
01            - 32.00   30.63     993.63
02            - 32.00   30.59     992.22
....
52            - 32.00   25.59     824.61
....
103                                31.04
104           - 32.00     .96        .00

A whopping 160.096686...% annual, compounded weekly...