Question

A savings loan offers 6% compounded quarterly. What is the effective rate to two decimal places? O 6.40% O 6.23% O 6.14% 0 6.27%

158

likes
789 views

Answer to a math question A savings loan offers 6% compounded quarterly. What is the effective rate to two decimal places? O 6.40% O 6.23% O 6.14% 0 6.27%

Expert avatar
Seamus
4.9
82 Answers
The formula for the effective annual rate (EAR) is:

EAR = \left(1 + \frac{r}{n}\right)^n - 1

Where:
- \( r \) = nominal annual interest rate (0.06 for 6%)
- \( n \) = number of compounding periods per year (4 for quarterly)

Step 1: Substitute the given values into the formula.

EAR = \left(1 + \frac{0.06}{4}\right)^4 - 1

Step 2: Calculate \(\frac{0.06}{4}\):

\frac{0.06}{4} = 0.015

Step 3: Add 1 to the result of Step 2:

1 + 0.015 = 1.015

Step 4: Raise the result of Step 3 to the power of 4:

(1.015)^4

Step 5: Calculate the power:

(1.015)^4 \approx 1.06136

Step 6: Subtract 1 from the result of Step 5 to find EAR:

1.06136 - 1 = 0.06136

Step 7: Convert the result to a percentage:

0.06136 \times 100 \approx 6.14\%

Therefore, the effective rate is:

6.14\%

Frequently asked questions (FAQs)
What is the radian measure of an angle that measures 45 degrees?
+
Math question: Solve the inequality -3x + 2 < 10 for x.
+
Convert 4.5 x 10^6 to standard notation.
+
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(𝑥, 𝑦) = 𝑥 sin 𝑦 at (1,0) in the direction of the unit vector that make an angle of 𝜋/4 with positive 𝑥-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 𝑌 = 2𝑋^2 − 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 DG⊥BG. If the area of the quadrilateral AGBD is equal to s, show that AC·BD≥2·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 ∪ B) = 0.6, P(B ∪ ̄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?