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 resulting displacement when a vector of magnitude 15 units is added to a vector of magnitude 20 units, given that they are in opposite directions?

Question: What is the vertex form equation of a quadratic function that has a vertex at (-3, 2)?

Solve for x: 3x + 5 = 20

New questions in Mathematics

A sample is chosen from a population with y = 46, and a treatment is then administered to the sample. After treatment, the sample mean is M = 47 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?

The strength of Kefexin oral suspension is 100 mg/ml. Nora has been prescribed cefalexin at a dose of 50 mg/kg/day divided in two single doses. Nora weighs 14 kg. How many milliliters of solution for Nora should be given as a single dose?

What is the coefficient of elasticity of the material that must be placed on the heel of the 10 cm high clog, with a base area of 2 cm² so that it deforms only 2 cm when the force on it will be a maximum of 600 N.

Karina has a plot of 5,000 square meters in which she has decided that 60% of it will be used to plant vegetables. Of this part, 12% will be dedicated to planting lettuce. How much surface area of the plot will be used for cultivation?

5) A family with a father, mother and 3 children must sit on five chairs in a row and the only restriction is that the mother must be at one end. In how many different ways can they be seated?

Evaluate limx→∞tan−1(x) using that y=tan−1(x) exactly when x=tan(y) . (Hint: Both tan and tan−1 are continuous!)

math question a bookstore announces a promotion valid for the same purchase as follows: buy a book and get 10% off the total purchase! buy two books and get 20% off your total purchase! buy three or more books and get 30% off your total purchase! Marcelo wanted to buy three books that cost 20.00 each without discount but he decided to buy two books in one day and another purchase with the third book the next day. If he had bought the three books at once he would have saved the following amount.

a bank finds that the balances in its savings accounts are normally distributed with a mean of $500 and a standard deviation off of $40. What is the probability that a randomly selected account has a balance of more than $400?

Let f(x) = x² − 1. Find the equation of the tangent line to the graph of f at the point x0 = 2.