Basic Math & Time Value of Money: Exercises
7. Present value. Assume you have an annual discount factor of 0.95. You own a perpetuity and an annuity, both of which pay $100 annually. The annuity matures after 50 annuals. Compute the present value of the stream of returns for both assets. Recall the following definitions.
\[\sum_{i=1}^{\infty} C \delta^{i} = C \frac{\delta}{1-\delta} \]
\[\sum_{i=1}^{N} C \delta^{i} = C \frac{\delta - \delta^{N+1}}{1-\delta} \]
# Use stock_prices to define vector sp500.
sp500 <- stock_prices$___
# Compute present value of annuity.
annuity_present_value <- 100*___/(1-___)
# Compute present value of perpetuity.
perpetuity_present_value <- ___*(0.95-0.95^___)/(1-___)
# Print present values of perpetuity and annuity.
print(perpetuity_present_value)
___
# Compute present value of annuity.
annuity_present_value <- 100*0.95/(1-0.95)
# Compute present value of perpetuity.
perpetuity_present_value <- 100*(0.95-0.95^51)/(1-0.95)
# Print present values of perpetuity and annuity.
print(perpetuity_present_value)
print(annuity_present_value)
test_error()
test_object("annuity_present_value", incorrect_msg="Did you use the formula for an infinite geometric series?")
test_object("perpetuity_present_value", incorrect_msg="Did you use the formula for a finite geometric series?")
test_function("print", incorrect_msg="Did you use the `print()` function?")
success_msg("Well done! How large was the difference between the two present values?")
Check the formulas for geometric series in the description.
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