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As a savings plan for college, when Arwyne was born, his parents deposited $25,207 in an account paying 6% compounded annually. How much is the interest earned from this investment after 18 years?

Question

As a savings plan for college, when Arwyne was born, his parents deposited $25,207 in an account paying 6% compounded annually. How much is the interest earned from this investment after 18 years?

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Solution

To solve this problem, we will use the formula for compound interest, which is:

A = P (1 + r/n)^(nt)

Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years

In this case, we have: P = $25,207 r = 6% or 0.06 (in decimal form) n = 1 (since the interest is compounded annually) t = 18 years

Substituting these values into the formula, we get:

A = 25,207(1+0.06/1)(118)A=25,207 * (1 + 0.06/1)^(1*18) A = 25,207 * (1.06)^18 A = 25,2072.8983A=25,207 * 2.8983 A = 73,082.79

The interest earned is the final amount minus the initial principal:

Interest = A - P Interest = 73,082.7973,082.79 - 25,207 Interest = $47,875.79

So, the interest earned from this investment after 18 years is $47,875.79.

This problem has been solved

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