1. ## Maturity value

Payments of $1800 and$2400 were made on a $10 000 variable-rate loan 18 and 30 months after the date of the loan. The interest rate was 11.5% compounded semiannually for the first two years and 10.74% compounded monthly thereafter. What amount was owed on the loan after three years? 10 000 1800 2400 ? {________________________|_________________|______ |___|______________________| 18 months 24months 30months 36months <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< >>>>>>>>>>>>>>>>>>>>>>>>>>>> 11.5% / 2 10.74/12 ( for the first 18 months the interest rate is 11.5% compounded semi annually after 6 months which is month number 24 the interest rate is 10.74% compounded annually ) FV = PV ( 1 + i ) ^ n 10 000 ( 1 + 11.5/2 ) ^ 2 * ( 1.5 ) 16 774.59 16 774.59 - 1800 = 14 974.59 14 974.59 ( 1 + 0.115/2 ) ^ 2 ( 0.5 ) 8 373.09 8 373.09 ( 1 + 0.4074/12 ) ^ 0.5 * 12 100 925.71 100 925.71 - 2400 = 98 525.71 98 525.71 ( 1 + 0.1074 / 12 ) ^ 0.5 * 12 1 187 587.57 I don't know if i did this correctly if not then where did i go wrong? 2. Your second line should be $10,000\ \times\ (1+0.115/2)^3$, since it's being compounded over 3 semiannual periods (18 months). Similarly, the multiplier in your 5th line should be (1 + 0.115/2), as you're dealing with one 6-month compounding period. In both the 7th and 10th lines, there are 6 one-month compounding periods, so your multiplier on both of these lines should be $(1+0.1074/12)^6$. Give that a spin and check back in with what you've got. 3. If it's easier for you: look at it as depositing$10,000 in a savings account,
then withdrawing $1,800 after 18 month,$2,400 after 30 months.

Also, always look for "reasonability"; like, for this result you got:
10 000 ( 1 + 11.5/2 ) ^ 2 * ( 1.5 )
16 774.59

It is impossible to earn over \$6,000 after 18 months at 11.5%;
10000 * .115 = 1150 (that's for a year!).

4. You need to do a major brush up on "Order of Operations". You really should.
Try this:

$
10,000\left( {1 + \frac{{0.115}}{2}} \right)^{\left( {2 \times 2} \right)} \left( {1 + \frac{{0.1074}}{{12}}} \right)^{\left( {1 \times 12} \right)}
$
$
- 1,800\left( {1 + \frac{{0.115}}{2}} \right)^{\left( {{\textstyle{1 \over 2}} \times 2} \right)} \left( {1 + \frac{{0.1074}}{{12}}} \right)^{\left( {1 \times 12} \right)}
$
$
- 2,400\left( {1 + \frac{{0.1074}}{{12}}} \right)^{\left( {{\textstyle{1 \over 2}} \times 12} \right)}
$

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