Question

An initial investment amount​ p, an annual interest rate​ r, and a time t are given. find the future value of the investment when interest is compounded​ (a) annually,​ (b) monthly,​ (c) daily, and​ (d) continuously. then find​ (e) the doubling time t for the given interest rate.

p=​$125,000​, r=3.4​%, t=3 yr


The future value of the investment when interest is compounded annually is $_____

Answer 1

To find the future value of an investment compounded annually, use the formula FV = Principal × (1 + interest rate)^time. With a principal of $125,000, a 3.4% interest rate, and over 3 years, the future value equals $138,181.87, and the compound interest earned is $13,181.87.

Step-by-step explanation:

The future value of an investment when interest is compounded is found using the formula:

FV = Principal × (1 + interest rate)^time

In this case, the principal (P) is $125,000, the annual interest rate (r) is 3.4% (or 0.034 in decimal form), and the time (t) is 3 years.

To find the future value for annual compounding, we would calculate it as follows:

FV = $125,000 × (1 + 0.034)^3

First, add 1 to the interest rate: 1 + 0.034 = 1.034.

Next, raise this sum to the power of the time, which is 3 years: (1.034)^3.

Then multiply the principal by the result to get the future value:

FV = $125,000 × 1.034^3 = $125,000 × 1.105454976 = $138,181.87

The compound interest is then calculated as the difference between this future value and the principal:

Compound interest = Future Value - Principal = $138,181.87 - $125,000 = $13,181.87.