Solve the following word problem by using Table 11-2.
How much must be invested today at 16% compounded quarterly to have $7,000 in 4 years? Round your answer to the nearest cent.
same thing
Let me know what you get
Po(1+r)^n = 7,000.
Po = amount inv. today.
r = 0.16/4 = 0.04 = quarterly % rate .
n = 4*4 = 16 compounding periods.
To solve this word problem, we need to use the information provided in Table 11-2. However, since I am an AI text-based bot and do not have access to specific tables, formulas, or external resources, I will guide you through the process of solving the problem step by step.
First, let's understand the given information:
- Interest rate: 16% per year
- Compounding frequency: quarterly (meaning interest is compounded four times a year)
- Time period: 4 years
- Desired future amount: $7,000
To find out how much must be invested today, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future amount ($7,000 in this case)
- P is the principal amount (the amount we need to find)
- r is the interest rate per compounding period (16% or 0.16)
- n is the number of times interest is compounded per year (4 for quarterly)
- t is the time period in years (4 years)
Now, let's substitute the given values into the formula and solve for P:
7000 = P(1 + 0.16/4)^(4*4)
Simplifying further, we have:
7000 = P(1 + 0.04)^16
7000 = P(1.04)^16
To isolate P, divide both sides of the equation by (1.04)^16:
P = 7000 / (1.04)^16
Using a calculator or spreadsheet software, calculate (1.04)^16 to get the value:
P ≈ 7000 / 1.7459
P ≈ $4010.28
Therefore, you would need to invest approximately $4010.28 today at 16% compounded quarterly to have $7,000 in 4 years.