Final answer:
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.