Pete's Real Estate is currently valued at $65,000. Pete feels the value of his business will increase at a rate of 10% per year, compounded semiannually, for the next 5 years. At a local fundraiser, a competitor offered Pete $70,000 for the business. If he sells, Pete plans to invest the money at 6% compounded quarterly. What price should Pete ask?

Verify your answer.

Note: LU12−I(2),LUI2−2(2) seems to be an incorrect or irrelevant notation and should be disregarded unless further context is provided.

Question

07-07-2024
Business

High School

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Pete's Real Estate is currently valued at $65,000. Pete feels the value of his business will increase at a rate of 10% per year, compounded semiannually, for the next 5 years. At a local fundraiser, a competitor offered Pete $70,000 for the business. If he sells, Pete plans to invest the money at 6% compounded quarterly. What price should Pete ask?

Verify your answer.

Note: LU12−I(2),LUI2−2(2) seems to be an incorrect or irrelevant notation and should be disregarded unless further context is provided.

Answer :

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pravinmca2002 pravinmca2002 · Answer 1 · 2025-03-02T07:29:08-05:00

Pete should ask for a price higher than $70,000 to ensure that the future value of his business, considering the compounding growth rate, exceeds the amount he would receive from selling and investing the money at the given interest rate.

To determine the price Pete should ask for, we need to calculate the future value of his business after 5 years with a growth rate of 10% compounded semiannually. Using the compound interest formula, the future value (FV) can be calculated as:

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

Where PV is the present value (initial value of the business), r is the annual interest rate (10% or 0.10), n is the number of compounding periods per year (2 for semiannual compounding), and t is the number of years (5).

FV = $65,000 * (1 + 0.10/2)^(2*5)

FV = $65,000 * (1 + 0.05)^10

FV = $65,000 * 1.628895

FV ≈ $105,886.18

Therefore, Pete should ask for a price higher than $105,886.18 to ensure that the future value of his business exceeds the amount he would receive from selling and investing the money at the given interest rate.

Based on the calculations, Pete should ask for a price higher than $105,886.18 to ensure that the future value of his business, considering the compounding growth rate, exceeds the amount he would receive from selling and investing the money at the given interest rate of 6% compounded quarterly.

Learn more about compounding here:

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