Financial Management

Self-Test Problems

ST-1        Assume that 1 year from now, you will deposit $1,000 into a savings account that pays 8%.

a. If the bank compounds interest annually, how much will you have in your account 4 years from now?

b. What would your balance 4 years from now be if the bank used quarterly compounding rather than annual compounding?

c. Suppose you deposited the $1,000 in 4 payments of $250 each at Year 1, Year

2, Year 3, and Year 4. How much would you have in your account at Year 4, based on 8% annual compounding?

d. Suppose you deposited 4 equal payments in your account at Year 1, Year 2, Year 3, and Year 4. Assuming an 8% interest rate, how large would each of your payments have to be for you to obtain the same ending balance as you calculated in part a?

a.

               [pic 1]                                                                                      n                                          3

If we put the money 1 year from now FV= PV( 1 + i )                =1000(1+8/100)        =1,259.712 $

By future value table under 8% and 3 on the left hand side        = 1000 x 1.260 = 1,260.00 $

b.

[pic 2]

                                                                                     N*M                                        3*4

If we put the money 1 year from now  FV = PV( 1 + i/M )                =1000(1+.08/4)        =1,268.2418 $

By future value table under 8% /2 = 2% and 12 on the left hand side        = 1000 x 1.268 = 1,268.00 $

c.

[pic 3]

                                              N                                              3

After year 1 FV = PV( 1 + i )                =250(1+.08)        = 314.93 $

                                              N                                              2

After year 2 FV = PV( 1 + i )                =250(1+.08)        = 291.60 $

                                              N                                              1

After year 3 FV = PV( 1 + i )                =250(1+.08)        = 270.00 $

                                              N                                              0

After year 4 FV = PV( 1 + i )                =250(1+.08)        = 250.00 $

        TOTAL                                                = 1,126.53 $

d.

X =?

1. Year one added X
2. Year 2, ( X + X *  ) = X + 1.08 X[pic 4]
3. Year 3, ( X + (X + 1.08X)  *  ) = 1.1664 X[pic 5]
4. Year 4, I know the FV,  ( X + (X + 1.08X + 1.1664 X) *  ) = 1.259712 X[pic 6]

X + 1.08X + 1.1664X + 1.259712 X = 1,259.72

4.506112 X = 1,259.72

X = 279.56 $

Problems

(2-1)        If you deposit $10,000 in a bank account that pays 10% interest annually, how much will be in your account after 5 years?

                           N                             5

  FV = PV( 1 + i )                =10000(1+i)        =16,105.1 $

By future value table under 10%  and 5 on the left hand side        = 10000 x 1.611 = 16,110.00 $