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.

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

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