MTH001 Assignment No. 2 Solution

Assignment # 2 (Lecture# 17 - 24) Of MTH001 (FALL 2010)

Maximum Marks: 30

Due Date:

January 24, 2011

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Question: 01 Marks: 10

Ali decides to invest a certain sum of money in business at the end of each year in the form of an annuity. He wants to get a sum of Rs.40, 000 after 20 years. If the payments accumulate at expected profit of 8% compound annually, how much should he start investing annually?

Question: 02 Marks: 10

Find the unknown values of , , and if and are multiplicative inverses of each other. Where .

Question: 03 Marks: 10

If and are the means for the two sets and respectively and related by and . Then find the values of ‘ ’ and ‘ ’.

.................

Solution 1):

This is a Future Value of an Ordinary Annuity problem.

Future Value is 40,000. Number of periods is 20. Annual rate is 8%

From TVM table for FV of an Annuity, the Factor is 45.7625

The FV = Annuity x Factor. We know the FV is 40,000, so divide it by the factor of 45.7625 to determine the Annuity amount of 874.08

The formula is ((1+ r)^n - 1) / r, or ((1.08)^20 - 1) / .08, or 4.661 - 1 = 3.661 / .08 = 45.7625