Business Math ( Future ordinary Annuities)
posted by Tracy
Howard has deposited RM1000 at the end of each month into a retirement savings plan for the last 10 years in his working life. His deposits earned an interest rate of 2.5% per month for the first 4 years and 3% per month for the rest of the years.
What is the accumulated value of his retirement savings plan?

Reiny
Think of it as 48 payments of 1000 at 2.5%, then that sum riding along for 72 periods at 3% plus 72 payments of 1000 for the next 72 periods
amount = 1000(1.025^48  1)/.025 (1.03)^72 + 1000(1.03^72  1)/.03
= 1,009,889.30 
Tracy
can i ask why the first four years need to multiply (1.03)^72

Reiny
You should get into the habit of making a time graph on a straight line for these kind of questions.
Think of the whole thing as being in two accounts.
1000(1.025^48)/.025 would be amount you would have at the end of 4 years, sitting at time 4
But you want that amount at time 10, with a new interest rate of 3%
So you have to find the future amount of the above value sitting at 4 accumulating at 3% for the next 6 years.
In your second account, my second term in the equation, thing of it as a new account starting at time 4 and going on for 72 months. 
Tracy
okay, i get it. Thanks for helping
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