Join thousands of students who trust us to help them ace their exams!Watch the first video
Multiple Choice
If $1 is invested today at an annual interest rate of 3.5\% compounded annually, how much will it be worth after 75 years?
A
$10.47
B
$5.25
C
$7.89
D
$10.12
Verified step by step guidance
1
Understand the concept of compound interest: Compound interest is calculated on the initial principal and also on the accumulated interest from previous periods. The formula for compound interest is \( FV = PV \times (1 + r)^n \), where \( FV \) is the future value, \( PV \) is the present value, \( r \) is the annual interest rate, and \( n \) is the number of years.
Identify the given values from the problem: \( PV = 1 \), \( r = 0.035 \) (3.5% annual interest rate), and \( n = 75 \) years.
Substitute the values into the compound interest formula: \( FV = 1 \times (1 + 0.035)^{75} \). This will calculate the future value of the investment after 75 years.
Simplify the expression inside the parentheses: \( 1 + 0.035 = 1.035 \). Then raise \( 1.035 \) to the power of \( 75 \) to account for compounding over 75 years.
Multiply the result of \( 1.035^{75} \) by the present value \( PV = 1 \) to find the future value \( FV \). This will give the amount the investment is worth after 75 years.