Question

1.1.7 Smith has just filed an income tax return and is expecting to re- ceive, in 60 days, a refund check of 1000. (a) The tax service that helped Smith fill out the return offers to buy Smith's refund check from Smith. Their policy is to pay 85% of the face value of the check. What annual simple in- terest rate is implied? (b) Smith negotiates with the tax service and sells the refund check for 900. To what annual simple interest rate does this correspond? (c) Smith decides to deposit the 900 in an account which earns simple interest at annual rate of 9%. What is the accumulated value of the account on the day Smith would have received his tax refund check? (d) How many days would it take from the time of his initial de- posit of 900 for the account to reach 1000?

Answer 1

Soutlon Amount of refund check payment received (1000 X 85%) Discount 1000 850 150 Amount of Interest % (150/850) This is for 60 days, so annualized 17.65% 1070 35% (17.65% X 365/60) rate Amount of refund check payment received now 1000 900 Amount of Interest (200/900) 11.11% This is for 60 days, so annualized rate 67.59% (11.11%8365/60) c) Amount of deposit 900 - Rate 9% уде м 60 мл 913.32 (900 +900x9%860/365 Amount of deposit 900 Rate % 1000 future value Interest amount Time = (100 (900x905)) TOD 1.23 years.