
Maturity value
Payments of $1800 and $2400 were made on a $10 000 variablerate 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?

Your second line should be $\displaystyle 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 6month compounding period.
In both the 7th and 10th lines, there are 6 onemonth compounding periods, so your multiplier on both of these lines should be $\displaystyle (1+0.1074/12)^6 $.
Give that a spin and check back in with what you've got.

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!).

You need to do a major brush up on "Order of Operations". You really should.
Try this:
$\displaystyle
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)}
$$\displaystyle
 1,800\left( {1 + \frac{{0.115}}{2}} \right)^{\left( {{\textstyle{1 \over 2}} \times 2} \right)} \left( {1 + \frac{{0.1074}}{{12}}} \right)^{\left( {1 \times 12} \right)}
$$\displaystyle
 2,400\left( {1 + \frac{{0.1074}}{{12}}} \right)^{\left( {{\textstyle{1 \over 2}} \times 12} \right)}
$
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