Yellow Sand Health just bought a new medical clinic for 1,940,488 dollars. To pa

Question

Yellow Sand Health just bought a new medical clinic for 1,940,488 dollars. To pay for the medical clinic, the company took out a loan that requires Yellow Sand Health to pay the bank a special payment of 19,380 dollars in 2 months and also make regular monthly payments forever. The first regular payment is expected in 1 month and all subsequent regular payments are expected to increase by 0.74 percent per month forever. The interest rate on the loan is 1.13 percent per month. What is the payment expected to be in 1 month?

Explanation / Answer

1. Computation of Present Value of Special Payment

Present Value = Payment / (1+0.0113^2)

Present Value = 19380 / (1+0.0113^2) = $18949.34

1. Computation of First Month payment

Total Loan - PV of Special payment = First Month payment * ( 1 + Growth Rate) / (Interest Rate - Growth rate)

1921538.67 = First Month payment * ( 1 + 0.0074) / (0.0113 - 0.0074)

1921538.67 * 0.0039 = First Month payment * 1.0074

7494 / 1.0074 = First Month Payment

First Month Payment = 7438.95

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