Question

Mira has saved $25,000 over the years and she has the option of investing it in either of the 2 investment plans. Investment A offers 12% interest compounded monthly, whereas Investment B pays 13% interest compounded semiannually. What would be the difference between the future values of the 2 investments if Mira's investment horizon is 7 years?

Answer 1

To compare the future values of Mira's investment options, we apply the compound interest formula to both Investment A (12% interest compounded monthly) and Investment B (13% interest compounded semiannually) over a 7-year period. Calculating the amount each investment will yield after 7 years will reveal the difference in their future values.

Step-by-step explanation:

Understanding Compound Interest

Mira has a choice between two investment plans. Plan A offers a 12% interest compounded monthly, while Plan B offers a 13% interest compounded semiannually. To compare the future values of these two investments over a 7-year investment horizon, we use the compound interest formula:

A = P(1 + r/n)^(nt)

For Investment A:

• 
  
• P = $25,000
• 
  
• r = 12% or 0.12
• 
  
• n = 12 (monthly)
• 
  
• t = 7

Future Value of Investment A: A = $25,000(1 + 0.12/12)^(12*7)

For Investment B:

• 
  
• P = $25,000
• 
  
• r = 13% or 0.13
• 
  
• n = 2 (semiannual)
• 
  
• t = 7

Future Value of Investment B: A = $25,000(1 + 0.13/2)^(2*7)

By calculating these, we will find the amount each investment yields after 7 years and can determine the difference between the future values of the two investments.