Question

You are a financial advisor with an investment company. The company has the following plans: Plan A :Where rate of interest is 12% per annum, compounded monthly overatime period of 3 months. Plan B :Where rate of interest is 12% per annum, compounded quarterly over a period of 3 months. Which plan would you advice your client to opt for if they want to invest 1,00,000 to make maximum profits?

Answer 1

Given :

For Plan A

Rate of interest , $r_1$ = 12% compounded monthly

Time period = $t_1$ = 3 months = 0.25 year

For Plan B

Rate of interest , $r_2$ = 12% compounded quarterly

Time period = $t_2$ = 3 months = 0.25 year

Total investment amount for both plan = Rs 1,00,000

To Find :

For maximum profit , which plan is advice

Solution :

From Compound Interest

∵ Amount = Principal × $(1+\dfrac{rate}{100})^{time}$

For Plan A

$A_1$ = Rs 1,00,000 × $(1+\dfrac{rate}{12\times 100})^{12\times time}$

   = Rs 1,00,000 × $(1+\dfrac{12}{12\times 100})^{12\times 0.25}$

   = Rs 1,00,000 × ( 1.01 )³

   = Rs 1,00,000 × 1.030301

   = Rs 103030.1

Similarly

For Plan B

$A_2$ = Rs 1,00,000 × $(1+\dfrac{rate}{4\times 100})^{4\times time}$

   = Rs 1,00,000 × $(1+\dfrac{12}{4\times 100})^{4\times 0.25}$

   = Rs 1,00,000 × ( 1.03 )1

   = Rs 1,00,000 × 1.03

   = Rs 103000

∴  By Comparing Amount for both the plan, we get

  $A_1$  $>$ $A_2$

i.e Amount for plan A $>$  Amount for plan B

Hence, For maximum profit, Plan A is better option . Answer