Business: 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.)

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Mira has saved $25,000 over the years and she has - id25000694332, hilzepesqtatiana

jay1462

12.03.2022

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

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