Compound Interest vs. Simple Interest: 7th Year Difference with $2,500 Investment

To calculate the difference in interest received in the 7th year between the account that pays simple interest and the account that pays compound interest, we need to use the formula for compound interest:

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

Where: A = the final amount P = the principal amount (initial investment) r = annual interest rate (as a decimal) n = number of times interest is compounded per year t = number of years

Given: Principal amount (P) = $2,500 Annual interest rate (r) = 9% or 0.09 (as a decimal)

For the account that pays simple interest, the interest received in the 7th year would be: Simple Interest = P * r * t Simple Interest = $2,500 * 0.09 * 7 Simple Interest = $1,575

For the account that pays compound interest, we need to know how many times interest is compounded per year. Let's assume it is compounded annually (n = 1). Compound Interest = A - P

Plugging the values into the compound interest formula: A = P(1 + r/n)^(nt) A = $2,500(1 + 0.09/1)^(1*7) A = $2,500(1 + 0.09)^7 A ≈ $4,035.36 (rounded to the nearest cent)

Compound Interest = A - P Compound Interest = $4,035.36 - $2,500 Compound Interest ≈ $1,535.36 (rounded to the nearest cent)

Therefore, you would receive approximately $1,535.36 more interest in the 7th year in the account that pays compound interest compared to the account that pays simple interest.