# Write 2 pages thesis on the topic mat105-0801b-13 business math. Objective: To describe and compute present value and future value of money and use this to prepare retirement plan for a person. Presen

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Write 2 pages thesis on the topic mat105-0801b-13 business math. Objective: To describe and compute present value and future value of money and use this to prepare retirement plan for a person. Present value of money: Present value of money is the value of a future receivable at present date. Let us take an example. Someone is going to receive $1000000 after ten years from now. The present value of this amount will be less than $1000000.

Future value of money: It is the value of a given amount of money at a future date. For example, someone is having $1000000 at present date. its value in future will be more than $1000000.

These are important concepts in financial planning of an individual and this is illustrated in the following example.

Let us plan for post retirement income of an individual. Currently he is earning $70,000 per annum and he will retire after 10 years. It can be reasonably assumed that he will need 60% of his present income after his retirement. This means he will need $42000 per annum after his retirement. It can be assumed that he will live for 20 years post retirement and therefore, by the time he retires he must have saved $42000*20 = $840000. He will need to accumulate this much amount before he retires that is within next 10 years. Therefore this amount, $840000 represents future value of his savings. Going by the prevailing interest rates it can be reasonably assumed that his savings will earn him an interest of 8% per annum compounding annually. Now the problem boils down to calculating his annual savings for the next 10 years.

Let us assume he decides to save $P each year, then

Future value (at retirement) of his first year’s savings = P(1+r)10

Future value (at retirement) of his second year’s savings = P(1+r)9

Future value (at retirement) of his third year’s savings = P(1+r)8

Future value (at retirement) of his fourth year’s savings = P(1+r)7

Future value (at retirement) of his fifth year’s savings = P(1+r)6

Future value (at retirement) of his sixth year’s savings = P(1+r)5

Future value (at retirement) of his seventh year’s savings = P(1+r)4

Future value (at retirement) of his eight year’s savings = P(1+r)3

Future value (at retirement) of his ninth year’s savings = P(1+r)2

Future value (at retirement) of his tenth year’s savings = P(1+r)

Adding all this leads to total savings at the retirement (A)

A = P[(1+r)10 + (1+r)9+ (1+r)8+ (1+r)7+ (1+r)6+ (1+r)5+ (1+r)4+ (1+r)3+ (1+r)2+ (1+r)]

Or, A = P(1+r)[(1+r)9-1]/r

Putting, A = $840000r = 8% = 0.08 results in

$910000 = 13.48656P

Hence P = $910000/13.48656 = 62285

This amount is almost 90% of his current income and it would be literally impossible to spare such a huge proportion of his income for saving for his retirement. This is primarily due to the fact that he started very late for his retirement and one should in fact start early for one’s retirement savings that reduces the burden to a great extent.

References

Cleaves, C. & Hobbs M. (2005). Compound Interest and Future Value, (7th ed.). Upper Saddle River, NJ: Prentice.

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