Keep the Highest: 3 Attempts: 7. Present value of annuities and annuity payments
ID: 2814152 • Letter: K
Question
Keep the Highest: 3 Attempts: 7. Present value of annuities and annuity payments The present value of an annuity is the sum of the discounted value of all future cash flows. Aa Aa You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)? Assume that all annuities earn the same positive interest rate. An annuity that pays $1,000 at the beginning of each year O An annuity that pays $1,000 at the end of each year An annuity that pays $500 at the beginning of every six months O An annuity that pays $500 at the end of every six months An ordinary annuity selling at $5,703.57 today promises to make equal payments at the end of each year for the next 10 years (N). If the annuity's appropriate interest rate (1) remains at 8.00% during this time, the annual annuity payment (PMT) will be You just won the lottery. Congratulations! The jackpot is $85,000,000, paid in 10 equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won assuming annual interest rate of 8.00%.Explanation / Answer
Q1) Option 1 - 1000 at the beginning of year
Time value of money - The largest sum at the earliest is better. So beginning period payment is better and among that 1000 is better .
Q2)
PMT = r(PV) / (1 - (1+r)^-n )
r = 8% ; PV= 5703.57 ; n = 10 years
PMT = 0.08 * 5703.57/ (1-(1.08)^-10)
= 850
( can be calculated using calculator or excel PMT formula) nper = 10 , r= 8%, PV = -5703.57 , FV=0
Q3)
Equal payments PMT = 85000000/10 = 8500000
N = 10
r = 8%
PV for payments in the beginning of the year = PMT * (1+r) [ 1- (1+r)^-10 ] / r
= 8500000 *1.08 *( 1-(1.08)^-10) / 0.08
= 61,598,547.24
(Or can be calculated using calculator / excel PV formula and then multiply by 1.08 since the payment is in the beginning)
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