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A local bank in town offers two types of savings plan with different interest rates to customers. Plan A offers an annual interest rate of 0.25% (0.0025) of the amount deposited. Plan B offers an annual interest of 0.2% of the amount deposited in the current year and 0.1% of the amount deposited two years back. Plan B will give 0.3% only for the first year of deposit. EXCEL Based on a retirement research article stated in a magazine, a minimum sum of $1 000 000 is required for one to retire comfortably. After reading the article, Ah Seng decides to deposit his $100 000 into the bank this year. Which plan should Ah Seng choose so that he is able to hit the $1 000 000 as quickly as possible without taking out his deposit at any point in time?

Respuesta :

mathmate
Assuming he had not dealt with the bank offering plan B before, he has nothing deposited two years back.  Hence plan B only gives him only 0.2% annual interest for his deposit.
Plan A gives 0.25% for his deposit all the time.
So plan A is more advantageous.

For durations, 
To reach $1,000,000 from $100,000, the money needs to grow 10 fold, or
(1+i)^n=10
n=log(10)/log(1+i).

So for plan A:
n=log(10)/log(1.0025)=922.18 years, while for

plan B
n=log(10)/log(1.0020)=1152.44 years.
 
Hope the bank(s) still exist at that time.