Snow White entered into a rental contract with the Queen on /115 and agreed to p

Question

Snow White entered into a rental contract with the Queen on /115 and agreed to pay $1,000,000 rent per year for the next 10 years. Equal payments are to be made semiannually on each January I and Jaly , starting January 1, 2015. On July 1. 2020, Snow White agreed to made a single payment im full settlement of all future obligations (including the payment tomade that day) Assuming a 6% nterest rate, how much should Snow White pay to settle the remaining obligation (rounded to the nearest dollar)? 131 r%or Onow poy

Explanation / Answer

Solution:

Semiannual payment of rent = $1,000,000 / 2 = $500,000

Total number of semiannaul payments =10*2 = 20

Semi annual payment made up to 01.07.2020 excluding payment to be made on 01.07.2010 = 11

Remaining semi annual payment on 01.07.2020 = 9

Rate of interest = 6%, semi annual rate =3%

Amount to be paid on 01.07.2010 to settle all future obligation = $500,000 * cumulative PV Factor for annuity due for 9 periods at 3%

= $500,000 * 8.019692 = $4,009,846

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