A perpetuity-due paying 5 every year has a present value of 50. An annuity-immed

Question

A perpetuity-due paying 5 every year has a present value of 50. An annuity-immediate paying 10 monthly for 5 years has the same effective rate of interest what is the present value of this Hint: To calculate the monthly annuity, you should find the present value of a 60 payment annuity using the monthly effective rate of interest that is equivalent to to the annual effective rate of interest that you derived from the perpetuity. That s find T]to align the payment with the interest conversion period O 448 O 460 Question 2 10 pts We wish to purchase a ten year annuity with 100.000. Given an effective rate of interest of 8%. What is the difference between the monthly payment for a monthly annuity-immediate and a monthly annuity-due? Hint: To calculate the monthly payments, you should find use annuity formulas with 120 payments, which use monthly effective rates of interest or discount that are equivalent to the annual effective rate of interest of 8%. 0 7.66 O 91.95 1.103.92 O 4473.39

Explanation / Answer

1) present value of perpetuity due = 50

let the effective rate for perpetuity = r

5/r = 50

r = 5/50 = 0.10 or 10%

monthly rate , i = r/12 = 10/12 = 0.83333% = 0.0083333

no. of months in 5 years , n = 5*12 = 60

payment in annuity , A = 10

Present value of annuity = A*PVIFA(60,0.83333%)

where PVIFA = present value interest rate factor of annuity

PVIFA(60,0.83333%) =[ (1+i)n -1]/((1+i)n *i)

= [ (1.0083333)60 -1]/((1.0083333)60 *0.0083333) = 47.06541262

Present value of annuity = 10*47.06541262 = 470.6541262 or 470.65 ( after rounding off to 2 decimal places)

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