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Senior | Next Rank: 100 Posts
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by MI3 » Wed Jun 01, 2011 5:15 am
Q: Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?
A. $506.00
B. $726.24
C. $900.00
D. $920.24
E. $926.24

I don't have the answer to this question, please opine.

Thanks,
M
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by Frankenstein » Wed Jun 01, 2011 5:20 am
Hi,
Principal --- Interest
1.)10000 200(2%)
2.)10200 306(3%)
3.)10506 420.24(4%)
--------------------------
Interest = 926.24

Hence, E
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by MI3 » Wed Jun 01, 2011 5:23 am
Hello Frankenstein,

I see that you have broken the problem in to three parts, each individually calculated using the formula PRT/100 (each applied for a six month duration). But, is there a direct formula that can be applied without breaking it up into parts?

Thanks,
M
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by Frankenstein » Wed Jun 01, 2011 5:26 am
MI3 wrote:Hello Frankenstein,

I see that you have broken the problem in to three parts, each individually calculated using the formula PRT/100 (each applied for a six month duration). But, is there a direct formula that can be applied without breaking it up into parts?

Thanks,
M
Hi,
You can perhaps try 10000(1+0.02)(1+0.03)(1+0.04) - 10000.
But, logically both are same. I am not sure whether this is what you are looking for.
Last edited by Frankenstein on Wed Jun 01, 2011 6:04 am, edited 1 time in total.
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by SoCan » Wed Jun 01, 2011 5:56 am
Frankenstein wrote:
MI3 wrote:Hello Frankenstein,

I see that you have broken the problem in to three parts, each individually calculated using the formula PRT/100 (each applied for a six month duration). But, is there a direct formula that can be applied without breaking it up into parts?

Thanks,
M
Hi,
You can perhaps try 10000(1+0.02)(1+0.03)(1+0.04) - 10000.
But, logically both are same. I am not sure if this is what you are looking for.
Yeah, the way I solved it was multiply (1.02)(1.03)(1.04) = 1.092624. Since the initial principal is 10,000, it's easy to spot the interest in dollars from there.

However, be careful - you can do it this way because the interest doesn't compound in the interim of each period, so even though the periods are of different lengths, it works out. If the interest compounded semiannually, you'd have a different answer because the second period is two 6 month periods.
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