For the following investment, calculate the present value (principal) and the compound interest. Use Table 11-2. Round your answers to the nearest cent.
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Compound Amount $130,000
Term of Investment 12 yrs
Nominal Rate 11%
Interest Compounded (annually)
Present Value $________
Compound Interest $________
same type again
Po(1+r)^n = 130,000.
Po = present value.
r = 0.11 = annual % rate.
n = 12 = the number of compounding periods.
I = P-Po = 130,000-Po.
To calculate the present value and compound interest, you can use the formula for compound interest:
Compound Interest = Compound Amount - Present Value
To calculate the present value, you can use the formula:
Present Value = Compound Amount / (1 + (Nominal Rate/Interest Compounded) )^(Term of Investment)
Let's calculate:
Compound Amount: $130,000
Term of Investment: 12 years
Nominal Rate: 11%
Interest Compounded: Annually
Using the formula for present value:
Present Value = $130,000 / (1 + (0.11/1))^(12)
Let's simplify the formula:
Present Value = $130,000 / (1 + 0.11)^(12)
Present Value = $130,000 / (1.11)^(12)
Present Value ≈ $46,312.95
So, the present value of the investment is approximately $46,312.95.
To calculate the compound interest:
Compound Interest = $130,000 - $46,312.95
Compound Interest ≈ $83,687.05
Therefore, the compound interest for the investment is approximately $83,687.05.
To calculate the present value and compound interest for this investment using Table 11-2, you need to follow a few steps:
Step 1: Identify the relevant factors from the problem:
Compound Amount = $130,000
Term of Investment = 12 yrs
Nominal Rate = 11%
Interest Compounded (annually)
Step 2: Locate the compound factor in Table 11-2:
Since the interest is compounded annually, you need to find the compound factor for 12 years and the nominal rate of 11%.
Step 3: Calculate the present value:
To find the present value, you divide the compound amount by the compound factor.
First, locate the compound factor for 12 years and 11% in Table 11-2. Let's say the compound factor is 'X'.
Present Value = Compound Amount / Compound Factor
Present Value = $130,000 / X
Step 4: Calculate the compound interest:
To find the compound interest, subtract the present value from the compound amount.
Compound Interest = Compound Amount - Present Value
Compound Interest = $130,000 - Present Value (from Step 3)
Step 5: Round your answers to the nearest cent:
Once you have the values, round them to the nearest cent as mentioned in the question.
So, to find the present value and compound interest, you need to locate the compound factor for 12 years and 11% in Table 11-2. Then, use the factor to calculate the present value and compound interest. Remember to round your answers to the nearest cent.