Question

Mira has saved $25,000 over the years and she has the option of investing it in either of the two investment plans. investment a offers 12 percent interest compounded monthly, whereas investment b pays 13 percent interest compounded semiannually. what would be the difference between the future values of the two investments if mira's investment horizon is seven years? (round your answer to two decimal places.)​

Answer 1

Answer: The difference in the two future values is $2703.79.

We arrive at the answer at follows:

We need to find the future value of these investments.

A. First investment Plan

We have

Principal                                                                              $25,000

Interest rate per year (i)                                                          12%

No. of years  (n)                                                                         7                            

No. of compounding periods per year (m)                             12 (monthly)

We can compute the Future Value (FV) of this investment with the following formula:

$FV = P * (1 + \frac{i}{m})^{m*n}$

Substituting the relevant values in the formula above we get,

$FV_{1} = 25000 * (1 + \frac{0.12}{12})^{12*7}$

$FV_{1} = 25000 * (1.01)^{84}$

$FV_{1} = 25000 * 2.306722744$

$FV_{1} = 57668.0686$

B. Second investment Plan

We have

Principal                                                                              $25,000

Interest rate per year (i)                                                          13%

No. of years  (n)                                                                         7                   No. of compounding periods per year (m)                      2 (semi-annual)

We can compute the Future Value (FV) of this investment with the following formula:

$FV = P * (1 + \frac{i}{m})^{m*n}$

Substituting the relevant values in the formula above we get,

$FV_{2} = 25000 * (1 + \frac{0.13}{2})^{2*7}$

$FV_{2} = 25000 * (1.065)^{14}$

$FV_{2} = 25000 * 2.414874185$

$FV_{2} = 60371.85461$

C. Difference between the two Future values

$Difference in FVs = FV_{2} - FV_{1}$

$Difference in FVs = 60371.85461 - 57668.0686$

$Difference in FVs = 2703.786013$