(a) What interest rate compounded monthly is equivalent to (has the same APY as) 15% compounded...

(a) What interest rate compounded monthly is equivalent to (has the same APY as) 15% compounded semi-annually? (b) What interest rate compounded continuously is equivalent to (has the same APY as) 15% compounded semi-annually?

Solutions

Expert Solution

(a) What interest rate compounded monthly is equivalent to (has the same APY as) 15% compounded semi-annually?

Effective Annual rate = ( 1 + Interest per period)^Periods per year] - 1

Effective Annual rate = 1.075^2 - 1

Effective Annual rate = 15.56%

Nominal Interest Rate Compounded monthly = (1 + Effective Interest Rate)^(1/Periods per year) - 1] * Periods per year

Nominal Interest Rate Compounded monthly = 1.1556^(1/12)-1] * 12

Nominal Interest Rate Compounded monthly = 1.01213-1] * 12

Nominal Interest Rate Compounded monthly = 14.55%

(b) What interest rate compounded continuously is equivalent to (has the same APY as) 15% compounded semi-annually?

Effective Annual rate = ( 1 + Interest per period)^Periods per year] - 1

Effective Annual rate = 1.075^2 - 1

Effective Annual rate = 15.56%

Nominal Interest Rate Compounded Continuously = Ln(1 + Effective Interest rate)

Nominal Interest Rate Compounded Continuously = Ln(1.1556)

Nominal Interest Rate Compounded Continuously = 14.46%

jeff jeffy answered 1 year ago

Next > < Previous

Related Solutions

What is the annual compounded monthly rate equivalent to 19% per annum compounded per quarter?

For an interest rate of 8% per year compounded monthly, what is the nominal interest rate...

For an interest rate of 8% per year compounded monthly, what is the nominal interest rate for one year?

What level rate of interest compounded annually is equivalent to 8% for the next 10 years...

What level rate of interest compounded annually is equivalent to 8% for the next 10 years and 5% for the following 10 years?

The annual interest rate on a credit card is 18% with interest compounded monthly. If a...

The annual interest rate on a credit card is 18% with interest compounded monthly. If a payment of $100 is made at the end of each month, how many months will it take to pay off an unpaid balance of $2,583.56 (assuming no additional purchases are made)?

An interest rate of 21% per year, compounded every 4 months, is equivalent to what effective...

An interest rate of 21% per year, compounded every 4 months, is equivalent to what effective rate per year? Show spreadsheet solutions

Bank A pays 15% interest, compounded monthly, on its money market account. What is the effective...

Bank A pays 15% interest, compounded monthly, on its money market account. What is the effective annual rate?

Which of the following APRs compounded monthly is equivalent to an APR of 14.15% compounded quarterly...

Which of the following APRs compounded monthly is equivalent to an APR of 14.15% compounded quarterly using 360-day calendar years, 30-day months, and 3-month quarters? a) 12.960% b) 13.320% c) 13.680% d) 14.040% e) 14.400%

Given a nominal interest rate of 6.5% compounded semi-annually, compute: a) The equivalent nominal rate of...

Given a nominal interest rate of 6.5% compounded semi-annually, compute: a) The equivalent nominal rate of discount compounded quarterly b) The equivalent constant force of interest

Calculate the equivalent periodic interest rate per payment interval for the following annuity Semi-annual payments earning 6% compounded monthly

Calculate the equivalent periodic interest rate per payment interval for the following annuity Semi-annual payments earning 6% compounded monthly O 5.00000% O 3.03775% O 3.08771% 0 2.97233% O 0.83161%

Find the effective interest rate fora) 10% compounded monthly?b) 12% compounded semiannually.

Subjects