Question

In: Finance

a debt of 500 dollars is paid 25 dollars every end of the year for 30...

a debt of 500 dollars is paid 25 dollars every end of the year for 30 years, if the borrower replaces the debt principal with a sinking fund that produces an effective annual interest rate of 1.5%, calculate the annual effective interest rate paid by the borrower on this debt. Choose the answer that is closest!

a) 1,54%
b) 2,43%
c) 2,90%
d) 3,54%
e) 3,90%

dont use excel!! manually!!

Solutions

Expert Solution

The correct answer is option d) 3,54%

We need not use excel, but we will have to use the financial calculator.

Straight Debt:

A debt of 500 dollars is paid 25 dollars every end of the year for 30 years,

If i is the interest rate then, use the financial calculator to calculate the interest rate.

i = ? when n = 30, PMT = 25, PV = -500, FV = 0

i = 2.8%

Sinking fund:

A sinking fund that produces an effective annual interest rate of j = 1.5% is good enough to take care of loan principal of $ 500 after 30 years.

Let's assume the contribution towards sinking fund per annum be S. Hence FV of S over 30 years should be good enough to take care of the loan of $ 500

Hence, S / j x [(1 + i)N - 1] = S / 1.5% x [ (1 + 1.5%)30 - 1] = 37.54S = 500. hence, S = 500 / 37.54 = 13.32

Annual interest portion = i x $ 500 = 2.8% x $ 500 = $ 14

Hence total annual payment per annum = interest portion + contribution towards sinking fund = 14 + 13.32 = 27.32

If i' is the annual effective interest rate paid by the borrower on this debt, then PV of all future payment at R should be the loan amount today.

Hence we have to find R. Use financial calculator:

i' = ?, n = 30, PMT = 27.32, PV = -500, FV = 0

i' = 3.54%

Hence, the correct answer is option d) 3,54%


Related Solutions

Calculate the present value of $1 million paid at the end of every year in perpetuity,...
Calculate the present value of $1 million paid at the end of every year in perpetuity, assuming a rate of return of 10% and a constant growth rate of 6%.
$1 is paid at the end of every year for 50 years. Assume an interest rate...
$1 is paid at the end of every year for 50 years. Assume an interest rate of 5% unless otherwise noted. 3. Calculate the value of the annuity at t = 25 using the following methods: 1. Sum up the value of each individual payment 2. Use the annuity formulas 3. Use the excel formulas 4. Accumulate the value from part 1.1 5. Present value the value from part 2.1 For 4, part 1.1 gives total present value of $18.2559....
Suppose a property has estimated real estate taxes for the current year of $4,398.25 dollars and that taxes are paid at the end of the year.
Suppose a property has estimated real estate taxes for the current year of $4,398.25 dollars and that taxes are paid at the end of the year. If the property is   being sold on May 25 in a year with 365 days and the buyer and seller agree to prorate the taxes at the time of closing with the buyer being responsible for theday of closing, what amount will be charged to the seller on the settlement statement?$1,000.00$1,735.20$2,663.05  None of the above
with the current US national debt being $21 trillion dollars, if it was all paid of...
with the current US national debt being $21 trillion dollars, if it was all paid of at once in $100 dollar bills, how many $100 dollars bills would it take and how much would those $100 dollar bills weigh in tons? this is the equvilant to how many loaded tractor trailer rigs (80000 # each) if the $100 bills were laid on the ground like a carpet how big of an area would it cover (square miles) assume that someone...
bob borrows $10,000 to be paid back over 30 years with level end of your year...
bob borrows $10,000 to be paid back over 30 years with level end of your year payments at an annual interest rate of x. The sum of principal repayment during year five and year 10 is equal to the amount of principle repaid during the year 15. find x
A debt must be settled in two years, through payments of 6000 dollars every two months...
A debt must be settled in two years, through payments of 6000 dollars every two months overdue. The debtor agrees with his creditor to restructure the debt liquidating the debt in 3 years and a half with equal monthly payments due. Calculate the value of the new payments, if the The effective interest rate is 13% per annum.
An annuity pays $1 at the end every odd year and $2 at the end of...
An annuity pays $1 at the end every odd year and $2 at the end of each even year (not counting year 0) for 10 years. If the effective annual rate is 6%, what is the present value of the annuity? Show all your work leading to your final answer
End of year two, sami withdrew 3200 dollars, and he deposited 2100 dollars end of year three. compute the last two payments.
sami is planning on buying a car after five years. the current price of the car is 50,000 dollars and inflation rate is 3 percent. sami currently has 11,000 dollars in a bank account that pays an annual interest rate of 8 percent, compounded semi-annually. he wants to save for the balance by making semi annual payments in the account, at the end of each period. 1.compute the amount of the paymentsEnd of year two, sami withdrew 3200 dollars, and...
a.) A series of 25 end-of-year deposits beginning with $1390 at the end of year 1...
a.) A series of 25 end-of-year deposits beginning with $1390 at the end of year 1 and increasing by $410 per year with a 8% interest rate. What Uniform Series of deposits would result in the same cumulative balance? b.) A series of 30 end-of-year deposits are made into an account that returns 4.2.% per year compounded annually. The first deposit is $5,251 and the deposits increase by 4.2% each year. How much will be in the account immediately following...
B. A series of 25 end-of-year deposits beginning with $1135 at the end of year 1...
B. A series of 25 end-of-year deposits beginning with $1135 at the end of year 1 and increasing by $260 per year with a 6% interest rate. What Uniform Series of deposits would result in the same cumulative balance? $ C. John makes 35 end-of-year deposits into a retirement account that returns 5.0.% per year compounded annually. His first deposit is $7500 and he increases the deposits by 8.9% each year. How much will be in the account immediately following...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT