Question

recall the equation for simple interest ( a = p(1 + rt) ). compare the amount of interest earned in 10 years for an investment of $1700 with a 7% annual simple interest rate and a 7% annual interest rate compounded annually.
simple interest: $
compound interest: $
the compound - interest investment earned $ more than the simple - interest investment.

Explanation:

Step1: Calculate Simple Interest

The formula for simple interest amount is \( A = P(1 + rt) \), where \( P = 1700 \), \( r = 0.07 \), \( t = 10 \).
\( A_{simple}=1700(1 + 0.07\times10)=1700\times1.7 = 2890 \)
Simple Interest \( I_{simple}=2890 - 1700 = 1190 \)

Step2: Calculate Compound Interest

The formula for compound interest (compounded annually) is \( A = P(1 + r)^t \), where \( P = 1700 \), \( r = 0.07 \), \( t = 10 \).
\( A_{compound}=1700(1 + 0.07)^{10}\approx1700\times1.967151\approx3344.16 \)
Compound Interest \( I_{compound}=3344.16 - 1700 = 1644.16 \)

Step3: Find the Difference

Difference \( = 1644.16 - 1190 = 454.16 \)

Answer:

Simple Interest: $\boldsymbol{1190}$, Compound Interest: $\boldsymbol{1644.16}$, Compound Interest earned $\boldsymbol{454.16}$ more than simple interest.