**Compounding Interest Problem***Question:*How many quarters will it take to triple an initial investment at an interest rate of 14% compounded quarterly?---To solve this, we'll use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]Where: - $ A $: the amount of money accumulated after n years, including interest.- $ P $: the principal amount (initial investment).- $ r $: the annual interest rate (decimal).- $ n $: the number of times interest is compounded per year.- $ t $: the time the money is invested for in years.In this scenario, the goal is to triple the investment, so $ A = 3P $. The interest rate $ r $ is 14% or 0.14 in decimal form, compounded quarterly, which means $ n = 4 $.Set up the equation:\[ 3P = P \left(1 + \frac{0.14}{4}\right)^{4t} \]\[ 3 = \left(1 + \frac{0.14}{4}\right)^{4t} \]Now, solve for $ t $ using logarithms:\[ \log(3) = 4t \cdot \log\left(1 + \frac{0.14}{4}\right) \]\[ t = \frac{\log(3)}{4 \cdot \log\left(1 + \frac{0.14}{4}\right)} \]Calculate the value of $ t $ to find the number of years, then convert to quarters. This is a practical example of how compound interest can significantly affect investments over time.

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How many quarters will it take to triple an initial investment at an interest rate of 14% compounded quarterly?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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