lab%202011.01.28%20solutions

lab%202011.01.28%20solutions - FNAN 301 Solutions to lab...

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FNAN 301 Solutions to lab problems – 1/28/2011 Group lab problem (Summer C 2010, quiz 1, question 2, version 2) Clint just deposited $19,500 in an account that will earn 8.1 percent per year in compound interest for 12 years. If Mona deposits $19,500 in an account in 1 year from today that earns simple interest, then how much simple interest per year must Mona earn to have the same amount of money in 12 years from today as Clint will have in 12 years from today? Timeline Time Today in 1 yr in 2 yrs in 3 yrs in 4 yrs in 5 yrs in 6 yrs in 7 yrs in 8 yrs in 9 yrs in 10 yrs in 11 yrs in 12 yrs Time 0 1 2 3 4 5 6 7 8 9 10 11 12 Clint invest 19,500 Mona invest 19,500 Mona re-time 0 1 2 3 4 5 6 7 8 9 10 11 Solve in 2 steps: 1. Compute how much Clint will have in 12 years 2. Compute the simple interest rate needed by Mona to have the same amount in 12 years 1. Compute how much Clint will have in 12 years With Clint, C 0 = 19,500; r = .081, and t = 12 In 12 years, Clint will have C 0 × (1+r) t = 19,500 × (1.081) 12 = $49,652.71 2. Compute the simple interest rate needed by Mona to have the same amount in 12 years If Mona deposits $19,500 in 1 year from today, and she wants to have $49,652.71 in 12 years, then she needs to earn total interest of $49,652.71 – $19,500 = $30,152.71 over the 11 years between 1 year from today and 12 years from today To earn $30,152.71 over 11 years, she needs to earn [$30,152.71 / 11] = $2,741.16 in interest per year, since the same amount of interest is earned each year with simple interest The simple interest rate would be equal to the interest earned per year divided by the initial amount of the investment = [$2,741.16 / $19,500] = 14.057% per year Alternatively, if you earn simple interest, then C 0 today will grow to be worth the following in t periods: C 0 × (1 + (simple interest rate per period × t)) Therefore, since Mona expects to deposit $19,500 in 1 year from today and she wants to have $49,652.71 in 12 years from today, which is 11 years later, the required simple rate can be found as $49,652.71 = $19,500 × (1 + (simple interest rate per period × 11)) 49,652.71 / 19,500 = 2.5463 = × (1 + (simple interest rate per period × 11)) 2.5463 – 1 = 1.5463 = simple interest rate per period × 11 1.5463 / 11 = .07997 = 14.057% = simple interest rate per year If Mona invests $19,500 in 1 year from today and earned simple interest of 14.057% per year, she would have the same amount in 12 years from today as Clint, who invested $19,500 for 12 years at 8.1 percent compound interest 1
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This note was uploaded on 02/16/2011 for the course FINANCE 301 taught by Professor Murray during the Spring '09 term at George Mason.

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lab%202011.01.28%20solutions - FNAN 301 Solutions to lab...

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