Question

Hannah wants to start a Wellness Center. She will need $181096 to get started. It will take time for the business to become profitable so she expects that she can repay $11570 each year for the first five years. Each year after that she will increase her payment by X so her 6th payment would be $11570+X, and the 7th would be $11570+2X. If the bank is charging 5.2%/year compounded annually, and the loan is a ten year loan what is the value of X? $ 18264.6 Incorrect: Your answer is incorrect. What would her final payment be on year 10?

Answer 1

ANSWER:

THE PRESENT WORTH WILL BE EQUATED TO ZERO AT 5.2% INTEREST.

PW = INITIAL INVESTMENT + ANNUAL PAYMENT(P/A,I,5) + ANNUAL PAYMENT + X (P/F,I,6) + ANNUAL PAYMENT + 2X (P/F,I,7) + ANNUAL PAYMENT + 3X (P/F,I,8) + ANNUAL PAYMENT + 4X (P/F,I,9) + ANNUAL PAYMENT + 5X (P/F,I,10)

PW = 0

INITIAL INVESTMENT = 181,096

ANNUAL PAYMENT = 11,570

X = ?

I = 5.2%

SINCE THE VALUES OF OF P/A AND P/F ARE NOT AVAILABLE IN THE TABLES, I HAVE SOLVED IT IN THE EXCEL.

0 = -181,096 + 11,570(P/A,5.2%,5) + 11570 + X (P/F,I,6) + 11570 + 2X (P/F,I,7) + 11570 + 3X (P/F,I,8) + 11570 + 4X (P/F,I,9) + 11570 + 5X (P/F,I,10)

181,096 = 11,570(P/A,5.2%,5) +11570 + X (P/F,I,6) + 11570 + 2X (P/F,I,7) + 11570 + 3X (P/F,I,8) + 11570 + 4X (P/F,I,9) + 11570 + 5X (P/F,I,10)

THE VALUE OF X WHEN SOLVED IN EXCEL COMES DOWN TO $9561.447

THEREFORE THE TENTH PAYMENT WILL BE = 11570 + 9561.447 * 5 = 11570 + 47,807.24 = $58,377.24

						X=	9,561
YEAR	0	1	2	3	4	5	6	7	8	9	10
INITIAL INVESTMENT	-181,096
REPAYMENT		11,570	11,570	11,570	11,570	11,570	21,131	30,693	40,254	49,816	59,377
NPV	$0.00

X HAS BEEN SOLVED BY ADDING X IN 6TH YEAR ANNUAL PAYMENT AND SUBSEQUENTLY FOR 7 , 8 , 9 AND 10 YEARS AND BY TRIAL AND ERROR WE FOUND OUT THE VALUE OF X TO BE $9,561.447