Question

1.Find the following values, using the equations, and then work the problems using a financial calculator to check your answers. Disregard rounding differences. (Hint: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.)

a. An initial $400 compounded for 1 year at 8.8%. Round your answers to the nearest cent.
$  
b.An initial $400 compounded for 2 years at 8.8%. Round your answers to the nearest cent.
$  
c.The present value of $400 due in 1 year at a discount rate of 8.8%. Round your answers to the nearest cent.
$  

d..The present value of $400 due in 2 years at a discount rate of 8.8%. Round your answers to the nearest cent.
$  

2. Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1, so they are ordinary annuities. Round your answers to the nearest cent. (Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press FV, and find the FV of the annuity due.)

a $200 per year for 10 years at 8%.
$  
b. $100 per year for 5 years at 4%.
$  
c. $200 per year for 5 years at 0%.
$  

Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

d. $200 per year for 10 years at 8%.
$  
e. $100 per year for 5 years at 4%.
$  
f. $200 per year for 5 years at 0%.
$  

Answer 1

Note: From the words "compounded", it is assumed that it is compounded annually, and not semi-annually or quarterly or monthly or continuously. If otherwise, kindly make mention of the same, and I shall rework the answer accordingly.

1.
a) $435.20 [that is, $400 x 1.088]
b) $473.50 [that is $400 x 1.088 x 1.088, and rounded the final value to 2 decimal places]
c) $367.65 [that is $400 / 1.088, and rounded to 2 decimal places]
d) $337.91 [that is $400 / 1.088² and rounded to 2 decimal places]

2.
a) $2,897.31 [that is $200 x 1.08¹⁰ x [Sum of 1/1.08ⁿ where n = 1 to 10].
b) $541.63 [that is $100 x 1.04⁵ x [Sum of 1/1.04ⁿ where n = 1 to 5]
c) $1,000 [that is $200 x 1⁵ x Sum of 1/1ⁿ where n = 1 to 5]

d)  $3,129.10 [that is $200 x [1.08¹¹ x (Sum of 1/1.08ⁿ where n = 1 to 11) - 1].
e) $563.30 [that is $100 x [1.04⁶ x (Sum of 1/1.04ⁿ where n = 1 to 6) - 1]
f) $1,000 [that is $200 x (1⁶ x Sum of 1/1ⁿ where n = 1 to 6) -1]

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