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stepladder [879]
1 year ago
9

A local company has K2,500 to set up an annuity to be paid quarterly for 5 years. The payments of that annuity are to be increas

ed in line with the current interest rate. The account pays interest at 10% p.a. compounded quarterly,
a) Calculate the size of each payment during the first year.

b) What is the size of the final payment (payment at the end)?​
Mathematics
1 answer:
Anvisha [2.4K]1 year ago
3 0

Answer:

Step-by-step explanation:

(a).

Within 1 year, there would be 4 payments to be made.

therefore, PMT= \frac{P(1+i)}{n} = \frac{2500(1+0.025)}{4*5} =\frac{2562.5}{20} = $128.125

(i) 1st payment will be :PMT $128.125

(ii) 2nd payment will be :128.125*(1.025)^1= $131.33

(iii) 3rd payment will be :128.125*(1.025)^2=$134.61

(iv) 4th payment will be :128.125*(1.025)^3=$137.98

Hence the payments are: $128.125, $131.33, $134.61, and $137.98.

(b).

The size of the final payment PMT(1+i)^{m-1} where m 4 *5= 20

=128.125(1+0.025)^{20-1} \\=128.125(1.025)^{19} \\=$204.83

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DochEvi [55]

Answer:

a) The lowest test score that a student could get and still meet the colleges requirement is 27.0225.

b) 156 would be expected to have a test score that would meet the colleges requirement

c) The lowest score that would meet the colleges requirement would be decreased to 26.388.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 21.5, \sigma = 4.7

a. Find the lowest test score that a student could get and still meet the colleges requirement.

This is the value of X when Z has a pvalue of 1 - 0.12 = 0.88. So it is X when Z = 1.175.

Z = \frac{X - \mu}{\sigma}

1.175 = \frac{X - 21.5}{4.7}

X - 21.5 = 1.175*4.7

X = 27.0225

The lowest test score that a student could get and still meet the colleges requirement is 27.0225.

b. If 1300 students are randomly selected, how many would be expected to have a test score that would meet the colleges requirement?

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0.12*1300 = 156

156 would be expected to have a test score that would meet the colleges requirement

c. How does the answer to part (a) change if the college decided to accept the top 15% of all test scores?

It would decrease to the value of X when Z has a pvalue of 1-0.15 = 0.85. So X when Z = 1.04.

Z = \frac{X - \mu}{\sigma}

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Answer:

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Step-by-step explanation:

Yes, that's correct:

A = (1/2)(base)(height)

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