1) (Effective interest Rate) A stor will give you a 3% discount on the cost of y
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Question
1) (Effective interest Rate) A stor will give you a 3% discount on the cost of your purchase if you pay cash today. otherwise, you will be billed the full price with payment due in 1 month. what is the implicit borrowing rate being paid by custoers who choose to defer payment for the month?
2)( effective interest rate) You invest 1000$ at a 6% annual interest rate, stated as an APR, interest is compounded monthly. how much will you have in 1 year? in 1.5 year ?
3)(effective interest rate) In a discount interest loan, you pay the interest payment up front. For example, if a 1-year loan is stated as 10,000$ and the interest rate is 10%, the borrower "pays" .10 * $10,000 = $1000 immediately, thereby receiving net funds of $9000 and repaying $10,000 in a year.
a) what is the effective interest rate on this loan ?
b) what is the effective annual rate on a 1-year loan with an interest rate quoted on a discount basis of 20% ?
please explain how do you get your answers
Explanation / Answer
Answer :-
1.) Let the Purchase price = $1.
If Pay Today = 1 - 3%(discount)
= $.97
If pay after one month
The Deferred Payment as Saving a Cash Flow of $.97 Today, But Paying $1 in a month.
Monthly rate (r) = .03 / .97
= .0309
n = compounding on monthlty basis
Effective Annual interest rate = ( 1 + r)n - 1
= (1+.0309)12 - 1
= (1.0309)12 - 1
= 1.44078 - 1
= .44078
= 44.078%
2.) Amount Invested = $1000
Interest rate (r) = 6% per annuam
Compounding = monthly basis
Interest rate (r) = 6 / 12 = .5% on monthly basis
let Year (n) = 1 year (12 months)
Future Value = 1000 (1+r)n
= 1000 (1+.005)12
= 1000 * 1.062
= $1062
let Year (n) = 1.5 year (18 months)
Future Value = 1000 (1+r)n
= 1000 (1+.005)18
= 1000 * 1.094
= $1094
3.) a.) Loan amount = 10000
Interest rate = 10%
Interest amount = 10000*10%
= 1000
Net fund = 10000 - 1000
= 9000
Effective interest rate = Interest amount / Net fund
= 1000 / 9000
= 11.11%
b.) Loan amount = 10000
Interest rate = 20%
Interest amount = 10000*20%
= 2000
Net fund = 10000 - 2000
= 8000
Effective interest rate = Interest amount / Net fund
= 2000 / 8000
= 25%
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