Question 1157833: If money is invested at an interest rate of 5.8 percent per year, find the annual percent yield (also known as the effective yield or APY) of the investment for the following compounding methods.
Enter your answer as a percent rounded to 3 decimal places.
(a) Annual:
Your answer is
(b) Semiannual:
Your answer is
(c) Monthly:
Your answer is
(d) Daily:
Your answer is
(e) Continuously:
* For continuous compounding, use the formula: Ymax = e r - 1.
Your answer is
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 5.8% per year is equal to .058 per year.
you take the percent and divide it by 100 to get the rate.
you take the rate and multiply it by 100 to get the percent.
the nominal interest rate per year is equal to 5.8% per year / 100 = .058 per year.
with discrete compounding, the formula for the effective interest rate per year is:
y = (1 + n/c) ^ c - 1
y is the effective interest rate per year.
n is the nominal interest rate per year.
c is the number of compounding periods per year.
for annual compounding, the formula becomes y = (1 + .058/1) ^ 1 - 1 = .058
for semi-annual compounding, the formula becomes y = (1 + .058/2) ^ 2 - 1 = .058841.
for monthly compounding, the formula becomes y = (1 + .058/12) ^ 12 - 1 = .0595669462.
for daily compounding, the formula becomes y = (1 + .058/365) ^ 365 - 1 = .0597101128.
this assumes there are 365 days in a year.
for continuous compounding, there is a different formula.
that formula is y = e^n - 1
y is the effective interest rate per year
n is the nominal interest rate per year.
the continuous compounding formula becomes y = e ^ (.058) - 1 = .0597149957.
note that the effective interest rate gets larger when the number of compounding periods per year gets larger.
the largest the effective interest rate can become, with a given nominal interest rate per year, is with continuous compounding.
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