Problem 9-11A Time Value of money concept The following situations involve the a

Question

Problem 9-11A Time Value of money concept
The following situations involve the application of the time value of money concept:
1. Jan Cain deposited $19,500 in the bank on January 1, 1993, at an interest rate of 11% compounded annually.
How much has accumulated in the account by January 1, 2010?
2. Mark Schultz deposited $43,200 in the bank on January 1, 2000. On January 2, 2010, this deposit has
accumulated to $84,974. Interest is compounded annually on the account. What rate of interest did Mark earn on
the deposit?
3. Les Hinckle made a deposit in the bank on January 1, 2003. The bank pays interest at the rate of 8%
compounded annually. On January 1, 2010, the deposit has accumulated to $30,000. How much money did Les originally deposit on January 1, 2003?
4. Val Hooper deposited $11,600 in the bank on January 1 a few years ago. The bank pays an interest rate of 10%
compounded annually, and the deposit is now worth $30,052. For how many years has the deposit been invested?

Explanation / Answer

1) Fv = pv*(1+r)^n = 19500 ( 1.14)^ 18 = $127599.3 Here time period = 1993 to 2010 = 18 years PV =Present value Fv= Future value 2) FV = PV(1+r)^n = PV(1+r)^n = FV =(1+r)^n = FV / PV = (1+r)^10 = $84974 / $43200 = 1+r = 1.966991 ^(1/10) r = 1.0699-1 = 6.99% here time n = from 2000 to 2010 = 10 years 3) Fv = 30000 r= 8% n= 7 pv = ? Pv = FV / (1+r)^ n = 30000 / (1.08)^7 = $17504.71 4) PV = 11600 FV= 30052 r = 10% n= ? PV =FV /( 1+r)^n (1+r)^n = FV / PV (1.10)^n = 30052 / 11600 1.10^ n = 2.59069 n log 1.10 = log 2.59069 n*0.04139=0.41341 n=0.41341/0.04139 = 9.98years thank you...

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