Ryan borrows X at an effective annual rate of 11.5% and makeslevel payments at the...

Ryan borrows X at an effective annual rate of 11.5% and makes level payments at the end of each year for n years. The interest portion of the final payment is 180.04. The total principal repaid as of time n-1 is 6185.47. The principal repaid in the first payment is Y. calculate Y.

Solutions

Expert Solution

Interest portion of each payment is the interest rate times on the unpaid loan balance

the interest portion of the last payment = 180.04

interest rate = 11.5 %

Unpaid loan balance for n year = 180.04 / 11.5 % = 1565.57

Its the last payment , so all the remaining principal amount paidoff . so principal portion amount of last payment is

= 1565.57 .

Total payment = 1565.57 + 180.04 = 1745.61

Each annual payment = 1745.61

Initial loan amount = Principal amount paid in n period payment (last payment) + total principal repaid as of n-1 period

initial amount of loan = 1565.57 + 6185.47 = 7751.04

Interest portion of the first payment = intial loan amount * interest rate = 7751.04 * 11.5 % = 891.37

principal portion (y) of the first payment = annual payment - interest portion amount

= 1745.61 - 891.37 = 854.24

Y = 854.24

jeff jeffy answered 2 years ago

Next > < Previous

Related Solutions

Fred is repaying a loan of X at a 4% annual effective rate. He makes payments...

Fred is repaying a loan of X at a 4% annual effective rate. He makes payments of 100 at the end of each year for 10 years, followed by payments of 200 for n years. The amount of interest in the 8th payment is 60. Determine X. Possible answers are: 1,140 or 1,970 or 1,360 or 1,740 or 1,870. Thanks

Tom borrows $100 at annual effective interest rate of 4% and agrees to repay it with...

Tom borrows $100 at annual effective interest rate of 4% and agrees to repay it with 30 annual installments. The amount of each payment in the last 20years is set at twice that in the first 10 years. At the end of 10 years, Tom has the option to repay the entire loan with a final payment $X, in addition to the regular payment. This will yield the lender an annual effective rate of 4.5% over the 10-year period. Calculate...

Roberto borrows $10,000 and repays the loan with three equal annual payments. The interest rate for...

Roberto borrows $10,000 and repays the loan with three equal annual payments. The interest rate for the first year of the loan is 4% compounded annually; for the second year of the loan the interest rate is 5% compounded annually; for the third year of the loan the interest rate is 6% compounded annually. a. Determine the size of the equal annual payments. b. Would interchanging the interest rates for first year and third year change the answer to part...

1. Sam borrows $1,000,000 by a mortgage with annual payments over 30 years at a rate...

1. Sam borrows $1,000,000 by a mortgage with annual payments over 30 years at a rate of 9.75% per annum interest. What are his annual payments? what is the remaining balance on his loan after 5 years? 15 years? Suppose that 10 years after Sam takes out the loan, the mortgage is sold to an investor who requires a 10.5% rate of return on investments, how much is the investor willing to pay for the loan?

What will your monthly payments be? What is the effective annual rate on this loan?

You want to buy a new sports coupe for $84,600, and the finance office at the dealership has quoted you a 7.1 percent APR loan for 48 months to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?Group of answer choices$2,017.84; 7.24 percent$2,017.84; 7.29 percent$2,017.84; 7.34 percent$2,029.78; 7.29 percent$2,029.78; 7.34 percent

A perpetuity makes payments at the end of each year at an annual effective rate of...

A perpetuity makes payments at the end of each year at an annual effective rate of 3.4%. The payment pattern is 3,2,1 (at the end of years 1, 2 and 3) and this pattern repeats for the balance of the perpetuity. Calculate the present value of the perpetuity at the beginning of the rst year. Please show all work.

Bob borrows 540,000 at annual effective interest rate 3%. She repays this loan by paying off...

Bob borrows 540,000 at annual effective interest rate 3%. She repays this loan by paying off only the interest due at the end of each year to the lender and depositing a level amount Q at the end of each year into a sinking fund account paying 6% APY. The goal is to accumulate the full balance of the loan amount in the sinking fund at the end of 10 years. a. Find the level sinking fund deposit. b. What...

1.a The annual interest rate is 8% with annual compounding. Please calculate effective annual rate, effective...

1.a The annual interest rate is 8% with annual compounding. Please calculate effective annual rate, effective semi-annual rate, effective quarterly rate, effective monthly rate, effective weekly rate (1 year = 52 weeks), effective daily rate (1 year = 365 days). 1.b The annual interest rate is 8% with monthly compounding. Please calculate effective monthly rate, effective annual rate, effective semi-annual rate, effective quarterly rate.

effective annual interest rate

You have received a loan from a bank with a quoted rate of 18 percent compounded monthly. What is the Effective annual interest rate of the loan?

A deposit of X is made into a fund which pays an annual effective interest rate...

A deposit of X is made into a fund which pays an annual effective interest rate of 8% for 5 years. At the same time, 2X is deposited into another fund which pays an annual effective rate of discount of d for 3 years. The amounts of interest earned over the 10 past years are equal for both funds. Calculate d.

Subjects