Complete the following using compound future value. (Use the Table 12.1 provided.) Note: Round your answers to the nearest cent.
| Time | Principal | Rate | Compounded | Amount |
| :------ | :-------- | :-------- | :--------- | :----- |
| 12 years | $15,000 | 3 1/2 % | Annually | |
Answer (1)
Identify the principal amount, interest rate, and time period.
Convert the interest rate to decimal form: r = 3.5% = 0.035 .
Apply the compound interest formula: A = P ( 1 + r ) n = 15000 ( 1 + 0.035 ) 12 .
Calculate the future value and round to the nearest cent: A = $22 , 666.03 .
Explanation
Understanding the Problem We are asked to calculate the future value of an investment using compound interest. We are given the principal amount, the interest rate, the time period, and the compounding frequency.
Identifying Given Information The principal amount is $15 , 000 . The interest rate is 3.5% per year, which can be written as 0.035 in decimal form. The time period is 12 years, and the interest is compounded annually.
Recalling the Compound Interest Formula The formula for compound interest is: A = P ( 1 + r ) n where:
A is the future value of the investment/loan, including interest
P is the principal investment amount (the initial deposit or loan amount)
r is the annual interest rate (as a decimal)
n is the number of years the money is invested or borrowed for
Applying the Formula and Calculating the Future Value Now, we substitute the given values into the formula: A = 15000 ( 1 + 0.035 ) 12 A = 15000 ( 1.035 ) 12 Calculating ( 1.035 ) 12 , we get approximately 1.51106865 . Therefore, A = 15000 × 1.51106865 A = 22666.02975 Rounding to the nearest cent, we get $22666.03.
Stating the Final Answer Therefore, the amount after 12 years is $$22,666.03.
Examples
Compound interest is a powerful tool for growing wealth over time. For example, if you invest $1000 ina re t i re m e n t a cco u n tt ha t e a r n s ana v er a g e ann u a l re t u r n o f 7% , co m p o u n d e d ann u a ll y , a f t er 30 ye a rs , yo u r in v es t m e n tw o u l d g ro wt o a pp ro x ima t e l y $7,612.26. This demonstrates the long-term benefits of compound interest and the importance of starting to invest early.
