Question

You are going to invest $5000 for 5 years. Choose the 3 scenarios which will yield the highest values.
Responses
A interest rate 4.1%, compounded monthlyinterest rate 4.1%, compounded monthly
B interest rate 4.2%, compounded quarterlyinterest rate 4.2%, compounded quarterly
C interest rate 3.95%, compounded continuouslyinterest rate 3.95%, compounded continuously
D interest rate 4%, compounded dailyinterest rate 4%, compounded daily
E interest rate 3.99%, compounded semiannuallyinterest rate 3.99%, compounded semiannually
F interest rate 4.3%, compounded every 2 months

Answer 1

To determine the scenarios that will yield the highest values, we need to calculate the future value (FV) of the $5000 investment for each scenario using the formula:

FV = P * (1 + r/n)^(n*t)

Where:
P = Principal amount ($5000)
r = Annual interest rate
n = Number of compounding periods per year
t = Number of years

Let's calculate the future value for each scenario:

A: interest rate 4.1%, compounded monthly
r = 4.1% / 100 = 0.041
n = 12
t = 5

FV(A) = 5000 * (1 + 0.041/12)^(12*5)

B: interest rate 4.2%, compounded quarterly
r = 4.2% / 100 = 0.042
n = 4
t = 5

FV(B) = 5000 * (1 + 0.042/4)^(4*5)

C: interest rate 3.95%, compounded continuously
r = 3.95% / 100 = 0.0395
n = Continuous compounding
t = 5

FV(C) = 5000 * e^(0.0395*5)

D: interest rate 4%, compounded daily
r = 4% / 100 = 0.04
n = 365
t = 5

FV(D) = 5000 * (1 + 0.04/365)^(365*5)

E: interest rate 3.99%, compounded semiannually
r = 3.99% / 100 = 0.0399
n = 2
t = 5

FV(E) = 5000 * (1 + 0.0399/2)^(2*5)

F: interest rate 4.3%, compounded every 2 months
r = 4.3% / 100 = 0.043
n = 6
t = 5

FV(F) = 5000 * (1 + 0.043/6)^(6*5)

Now let's calculate the future values for each scenario:

FV(A) ≈ $6,513.65
FV(B) ≈ $6,537.12
FV(C) ≈ $6,511.41
FV(D) ≈ $6,494.17
FV(E) ≈ $6,512.30
FV(F) ≈ $6,559.86

The three scenarios that will yield the highest values are B, C, and F.