Chapter 5

Multiple Choice Question   Which of the following is the formula for the present value of a growing annuity? (C is the payment to occur at the end of the first period, r is the interest rate, g is the rate of growth per period expressed as a percentage, and t is the number of periods for the annuity.) Multiple choice question. PV = C(r−g)C(r−g) (1−((1−g)(1−r))t)1−(1-g)(1-r)t PV = C(r−g)C(r−g) (1−((1+g)(1+r))t)1−(1+g)(1+r)t PV = C(r−g)C(r−g) (1−((1−g)(1+r))t)1−(1-g)(1+r)t PV = C(r−g)C(r−g) (1−((1+g)(1−r))t)

What is the interest rate “r” if PV=$1250 and the FV=$2150 in year t=10?

What is the PV?

Calculate the number of periods for the following present value, interest rate, and future value:PV=810 ; r:7% ; FV= 4,341a) 18.42b) 8.71c) 21.37d) 24.81

calculate future values

Calculate the rate of interest

What is the interest rate?

Activity 1.3 Complete the table below by finding the unknown. Principal Rate Time Interest Maturity Value 2.5 years 4 years P45,000 2% 1.2% 3% P4,560 P105,000 P114,450 Guide Questions: For the first set of values a. What unknown variable will you solve first? b. What formula will you use to find the missing values? For the second set of values a. Which among the missing components can be solved using the given? b. How will you solve the next missing component? For the third set of values a. What formula will you use to find the missing value? b. Which component can be solved first using the given?

5. Calculating Interest Rate. Find the interest rate implied by the following combinations of present and future values: ( LO4) Present Value Years Future Value $400 11 $684 $183 4 $249 $300 7 $300

Use factors and a spreadsheet to determine the interest rate per period from the following equation: 0 = -26,000 + 8,000(P/A,i∗,5) + 8,000(P/F,i∗,8) What is the interest rate per period? %

1) What is the future value at time t=3 for a present value of PV=$100 (e.g., t=0) if the interest rate is r=0.10 (e.g., r=10%)? 2) What is the future value at time t=18 for a present value of PV=$1525 (e.g., t=0) if the interest rate is r=0.085 (e.g., r=8.5%)? 3) What is the present value of a future value of FV=$500 at time t=5 if the interest rate is r=0.10 (e.g., r=10%)? 4) What is the present value for a future value of FV=$500,000 at time t=36 if the interest rate is r=0.05 (e.g., r=5%)? 5) What is the interest rate “r” if PV=$100 and the FV=$350 in year t=12? 6) What is the interest rate “r” if PV=$1250 and the FV=$2150 in year t=10? 7) How long will it take to double your investment if the interest rate is r=0.06 (r=6%)?8) How long will it take to increase your investment by 2.5 times if the interest rate is r=0.14 (r=14%)?9) Which is the better option if the interest rate is r=0.10 (r=10%)? Show all work used to arrive at your answer. a. Option I: Receive $1000 today at time…

Given the following, construct a choice table for interest rates from 0% to 100%. Year            X          Y 0             −$10     −$20 1                 15         28

Q2: Suppose the current 1-year spot rate is 3% and the forward rate from time 1 to time 2 consistent with the current term structure of interest rates is 2%. Determine the 2-year discount factor from time 2 back to time 0.

For each of the following, compute the present value: (Your answers should be positive values.) \table[[Present value,Years,Interest rate,Future value],[,17,9%,$16,832

Determine the future value of the following single amounts:                    Invested Amount         Interest Rate               No. of Periods1.                      $ 15,000                      6%                                   122.                         20,000                      8                                      103.                        30,000                      12                                     204.                        50,000                       4                                      12

which one is correct please confirm? QUESTION 31 What is the effective rate of interest on a CD that has a nominal rate of 9.5 percent with interest compounded monthly?   a. 9.86%   b. 9.93%   c. 10.02%   d. 9.74%

calculating present values for each of the following, compute the present value Year   interest rate   future valuE 6      5%                    15451 9       11                     51557 23      16                    886073 18      19                    55016