Question

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2. Beniamin Franklin left $1,000 to Massachusetts and the city of Boston when he died in 1790. He also gave same amount to Pennsylvania and the city of Philadelphia. The money was paid to Franklin when he held political office, but he believed that politicians should not be paid for their service. The money would be paid out in 1990, 200 years after Frankin's death, to be used to train young people as specified on the Franklin's will. By that time, the Pennsylvania bequest had grown to about $2 million; the Massachusetts bequest had grown to $4.5 million. What rate of return did the two states earn? Assume annual compounding. 3. Calculate EAR for following compounding periods. Your APR is 10%. Compounding period Number of times compounded Year EAR/EAIR/APY Quarter Month Day Hour

Answer 1

2) Amount = Principal *(1+ Interest rate) time period Pennsylvania bequest had grown to 2 million dollar Massachusetts bequest had grown to 4.5 Million dollar The interest rate earned = Interest earned 2000000 = 1000*(1+Interest rate)^200 4500000 = 1000*(1+ Interest rate) 200 1 + Interest rate = (2000000/1000)^(1/200) 1 + Interest rate = (4500000/1000)^(1/200) 1.03874 1.04296 Interest rate = 1.03874-1 Interest rate = 1.04296 - 1 0.03874 or 3.874% 0.04296 4.296%

EAR (1+rate/m)^(m) -1 Where m is the compounding frequency APR = 10% Compounding period Number of time comounded EAR Calculation EAR (%) Year 1 ((1+0.1/1)^1-1)*100 10.000 Quarter ((1+0.1/4)^4-1)*100 10.381 Month ((1+0.1/12)^12-1)*100 10.471 Day (assuming 365) 365 ((1+0.1/365)^365 -1) *100 10.516 Hour (365 days*24 hours) 8760 ((1+0.1/8760)48760-1)*100 10.517