Question

What is the present value of an annuity if payments of $434.00 are made at the end of every month for 15 years at an interest rate of 7.5% per year computed monthly?

175

likes

874 views

Answer to a math question What is the present value of an annuity if payments of $434.00 are made at the end of every month for 15 years at an interest rate of 7.5% per year computed monthly?

$Expert avatar$

Bud

4.6

96 Answers

Solution:

1. Given:

- Monthly payment: USD 434.00

- Number of years: 15

- Annual interest rate: 7.5%

- Number of compounding periods per year: 12

2. Convert the annual interest rate to a monthly interest rate:

- Monthly interest rate

r = \frac{7.5\%}{12} = \frac{0.075}{12}

- Monthly interest rate

r = 0.00625

3. Calculate the total number of payments:

- Total number of payments

n = 15 \, \text{years} \times 12 \, \text{payments/year}

- Total number of payments

n = 180

4. Use the present value of an annuity formula:

- Present Value (PV) formula:

PV = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)

- Where:

*

C = 434

(monthly payment)

*

r = 0.00625

(monthly interest rate)

*

n = 180

(total number of payments)

5. Substitute the values into the formula:

PV = 434 \times \left( \frac{1 - (1 + 0.00625)^{-180}}{0.00625} \right)

6. Calculate:

PV\approx46817.07

The present value of the annuity is approximately USD 46817.07.

Frequently asked questions (FAQs)

What is the measure of an angle formed by the intersection of two lines if their slopes are -3/4 and 2/3?

Math question: Find the limit as x approaches 2 of (3x-5)/(x+1)

Question: What is the limit as x approaches infinity of (ln(x))/(x^{e^x})?

New questions in Mathematics

Solution to the equation y'' - y' - 6y = 0

a ferry travels 1/6 of the distance between two ports in 3/7 hour. the ferry travels at a constant rate. at this rate, what fraction of the distance between the two ports can the ferry travel in one hour?

A circular park has a diameter of 150ft. A circular fence is to be placed on the edge of this park. Calculate the cost of fencing this park if the rate charged is $7 per foot. Use π = 3.14.

1/2x +3 <4x-7

two particles start at the origin and move along the x axis. for 0 <= t <= 10, their respective position functions are given by x1 = cos(t) and x2 = (e^-3t) + 1. for how many values of t do the particles have the same velocity?

How many percent is one second out a 24 hour?

Which of the following is the product of multiplying twenty-seven and twenty-five hundredths by nine and twenty-seven hundredths?

To celebrate the five-year anniversary of a consultancy specializing in information technology, the administrator decided to draw 3 different qualification courses among its 10 employees. Considering that the same employee cannot be drawn more than once, the total number of different ways of drawing among employees is:

2x2 and how much?

4x/2+5x-3/6=7/8-1/4-x

suppose random variable x follows poisson distribution with expected value 3. what is variance of x?

Let x be an integer. Prove that x^2 is even if and only if is divisible by 4.

48 kg of 30% sulfuric acid in a mixture of 10% and 40% sulfuric acid arose. How many kilograms were each of the original solutions?

When taking a test with m closed answers, a student knows the correct answer with probability p, otherwise he chooses one of the possible answers at random. What is the probability that the student knows the correct answer given that he answered the question correctly.

A post office has three categories of letters: 60% are from businesses, 30% are individual mail, and the remaining 10% are government mail. 5% of the letters from businesses have address errors, 10% of the individual mail has address errors, while 1% of the government mail has address errors. If we receive a letter with an address error, what is the probability that it is individual mail?"

Marc, Jean and Michelle have traveled a lot. Marc drove twice as much as Jean, but it was Michelle who drove the most with 100km more than Marc. They respected their objective of not exceeding 1350km of distance. How far did John drive?

Sodium 38.15 38.78 38.5 38.65 38.79 38.89 38.57 38.59 38.59 38.8 38.63 38.43 38.56 38.46 38.79 38.42 38.74 39.12 38.5 38.42 38.57 38.37 38.71 38.71 38.4 38.56 38.39 38.34 39.04 38.8 A supplier of bottled mineral water claims that his supply of water has an average sodium content of 36.6 mg/L. The boxplot below is of the sodium contents levels taken from a random sample of 30 bottles. With this data investigate the claim using SPSS to apply the appropriate test. Download the data and transfer it into SPSS. Check that your data transfer has been successful by obtaining the Std. Error of the mean for your data which should appear in SPSS output as 0.03900.. If you do not have this exact value, then you may have not transferred your data from the Excel file to SPSS correctly. Do not continue with the test until your value agrees as otherwise you may not have correct answers. Unless otherwise directed you should report all numeric values to the accuracy displayed in the SPSS output that is supplied when your data has been transferred correctly. In the following questions, all statistical tests should be carried out at the 0.05 significance level. Sample mean and median Complete the following concerning the mean and median of the data. mean = mg/L 95% CI: to mg/L Based upon the 95% confidence interval, is it plausible that the average sodium content is 36.9 mg/L? median: mg/L The median value is 36.9 mg/L. Skewness Complete the following concerning the skewness of the data. Skewness statistic = Std. Error = The absolute value of the skewness statistic less than 2 x Std. Error Therefore the data can be considered to come from a population that is . Normality test Complete the following summary concerning the formal testing of the normality of the data. H0: The data come from a population that normal H1: The data come from a population that normal Application of the Shapiro-Wilk test indicated that the normality assumption reasonable for sodium content (S-W( )= , p= ). Main test Using the guidelines you have been taught that consider sample size, skewness and normality, choose and report the appropriate main test from the following ( Appropriate ONE ) You have selected that you wish to report the one-sample t-test. H0: The mean sodium content equal to 36.9 mg/L H1: The mean sodium content equal to 36.9 mg/L Application of the one-sample t-test indicated that the mean is 36.9 mg/L (t( ) = , p = ). You have selected that you wish to report the Wilcoxon signed rank test. H0: The median sodium content equal to 36.9 mg/L H1: The median sodium content equal to 36.9 mg/L Application of the Wilcoxon signed rank test indicated that the median is 36.9 mg/L (z = , N = , p = ).

A candy manufacturer must monitor deviations in the amount of sugar in their products They want their products to meet standards. They selected a random sample of 20 candies and found that the sandard deviation of that sample is 1.7. What is the probabilty of finding a sample variance as high or higher if the population variance is actually 3277 Assume the population distribution is normal.

An export company grants a bonus of $100,000 pesos to distribute among three of its best employees, so that the first receives double the second and the latter receives triple the third. How much did each person receive?

f(r) = 1/r+9 find f(x^2) + 1

What is the present value of an annuity if payments of $434.00 are made at the end of every month for 15 years at an interest rate of 7.5% per year computed monthly?

Answer to a math question What is the present value of an annuity if payments of $434.00 are made at the end of every month for 15 years at an interest rate of 7.5% per year computed monthly?

You might be interested in