Question

What equal payments in 3 years and 5 years would replace payments of $42,500 and $60,000 in 7 years and 9 years, respectively? Assume money can earn 3.36% compounded quarterly. Round to the nearest cent

89

likes
443 views

Answer to a math question What equal payments in 3 years and 5 years would replace payments of $42,500 and $60,000 in 7 years and 9 years, respectively? Assume money can earn 3.36% compounded quarterly. Round to the nearest cent

Expert avatar
Hermann
4.6
120 Answers
To solve this problem, we first need to calculate the present value of the future payments and then determine the equal payments at the 3-year and 5-year marks that have the same total present value when discounted back to the present at the given interest rate of 3.36% compounded quarterly.

### Step 1: Calculate the quarterly interest rate
Given that the annual interest rate is 3.36%, the quarterly interest rate is:
r = \frac{3.36\%}{4} = 0.84\%
Converting to decimal form, we get:
r = 0.0084

### Step 2: Calculate the number of quarters for each payment
- 7 years = 28 quarters
- 9 years = 36 quarters
- 3 years = 12 quarters
- 5 years = 20 quarters

### Step 3: Calculate the present value (PV) of each future payment
The present value formula is given by:
PV = \frac{P}{(1 + r)^n}
where P is the payment, r is the quarterly interest rate, and n is the number of quarters.

Calculating the present values of the future payments:
- Present value of 42,500 due in 7 years is 33,625.56.
- Present value of 60,000 due in 9 years is 44,398.58.

### Step 4: Calculate the total present value
Adding the present values of the two future payments gives a total present value of $78,024.14.

### Step 5: Calculate the present value of the payments in 3 years and 5 years
We need to find equal payments that, when discounted back to the present at the interest rate, will match the total present value from step 4.

### Step 6: Solve for the equal payments ( P )
Setting up the equation:
P \times \left( \frac{1}{(1 + 0.0084)^{12}} + \frac{1}{(1 + 0.0084)^{20}} \right) = 78024.14

By solving the equation, we find that each equal payment should be approximately $44,573.97.

Therefore, the equal payments required at the 3-year and 5-year marks to match the total present value of the original future payments are approximately \ 44,573.97$ each.

Frequently asked questions (FAQs)
What is the probability of rolling a three on a fair six-sided die?
+
Math question: Solve the inequality 3x + 5 < 25 for x.
+
What is 3 raised to the power of 4, multiplied by 5, minus the square root of 16?
+
New questions in Mathematics
A normal random variable x has a mean of 50 and a standard deviation of 10. Would it be unusual to see the value x = 0? Explain your answer.
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 person who weighs 200 pounds on earth would weigh about 32 pounds on the moon. Find the weight of a person on earth who would weigh 15 pounds on the moon.
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?
I) Find the directional derivative of 𝑓(π‘₯, 𝑦) = π‘₯ sin 𝑦 at (1,0) in the direction of the unit vector that make an angle of πœ‹/4 with positive π‘₯-axis.
Suppose the horses in a large stable, have a mean weight of a 807 pounds and a variance of 5776. What is the probability that the mean weight of the sample of horses with differ from the population mean by greater than 18 pounds is 41 horses are sampled at random from the stable round your answer to four decimal places.
Suppose SAT reading scores are normally distributed with a mean of 496 and a standard deviation of 109. The University plans towards scholarships for students who scores are in the top 7%. What is the minimum score required for the scholarship round your answer to the nearest whole number.
Log(45)
Suppose that you use 4.29 g of Iron in the chemical reaction: 2Fe(s) + 3 Cu2 + (aq) 2Fe 3 + (aq) + 3Cu(s ) - . What is the theoretical yield of Cu (s), in grams?
sum of 7a-4b+5c, -7a+4b-6c
In a 24 hours period, the average number of boats arriving at a port is 10. Assuming that boats arrive at a random rate that is the same for all subintervals of equal length (i.e. the probability of a boat arriving during a 1 hour period the same for every 1 hour period no matter what). Calculate the probability that more than 1 boat will arrive during a 1 hour period. (P(X>1) ) Give your answers to 4 decimal places and in a range between 0 and 1
Let X be a discrete random variable such that E(X)=3 and V(X)=5. Let π‘Œ = 2𝑋^2 βˆ’ 3𝑋. Determine E(Y).
find missing measure for triangle area = 48 m square base = 10m heaighy = ? m
Total Users with an active Wise account = Total Active Users + Total Users who haven’t transacted Total Active Users = Total MCA Users + Total Send Users = Total New Users + Retained Users Total New Users = New Send Users + New MCA Users Total MCA Users = New MCA Users + Retained Users who transacted this month via MCA Total Send Users = New Send Users + Retained Users who transacted this month via Send Send CR = Total Send Users / Total Users with an active Wise account MCA CR = Total MCA Users / Total Users with an active Wise account New Send CR = New Send Users / New Profiles Created in Month New MCA CR = New MCA Users / New Profiles Created in Month We have recently witnessed a drop in MCA conversion, but send user conversion is stable, can you help explain why?
Let G be the center of gravity of triangle ABC. We draw through A a parallel to BC on which we take a point D so that DGβŠ₯BG. If the area of the quadrilateral AGBD is equal to s, show that ACΒ·BDβ‰₯2Β·s.
To paint a 250 m wall, a number of workers were employed. If the wall were 30 m longer, 9 more workers would be needed. How many were employed at the beginning?
How much does 7.2 moles of ammonium dichromate weigh? (NH4)2Cr2O7
question 1 Consider a sample space S, and two events A and B such that P(A ∩ B) = 0.2, P(A βˆͺ B) = 0.6, P(B βˆͺ Μ„A) = 0.8 (a) [0.5 points] Calculate P (A). (b) [0.5 points] Calculate P (B)
Find the distance from the point (2,-1) to the line 2x-5y+10=0
Mark is gluing a ribbon around the sides of a picture frame. The frame is 11 inches long and 7 includes wide. How much ribbon does Mark need?