Jack would like to save now for 3 targets. First of all, he is planning to organ
ID: 2364127 • Letter: J
Question
Jack would like to save now for 3 targets. First of all, he is planning to organize a 20th Wedding Anniversary surprise party for his lovely wife Pearl 6 years from now. He will invite all their family members and friends to celebrate with them and it would cost $100,000. Second, Jack plans to buy a car in 2 years at a cost of $400,000. Third, he would like to withdraw $50,000 per year for 10 years for travelling, with the first withdrawal one year right after their 20th Wedding Anniversary. If his savings account offers him an interest of 10% compounded semi-annually, how much does he need to deposit today (in a lump sum)?Explanation / Answer
We need to calculate the PV of variou expenses. 1. Wedding anniv: 6 yrs from now so nper =6*2=12, i=10%/2 = 5%, FV=$100,000 So PV = FV/(1+i)^n = 100000/(1+10%/2)^12 = $55,684 2. Car 2 yrs from now so nper = 2*2, i=10%/2, FV=400000 So PV=FV/(1+i)^n = 400000/(1+10%/2)^4 = $329,081 3. n=10*2yrs, i=10%/2, PMT=50000. So PV at t6 (at 20th anniv) = PV(rate,nper,-pmt) ie PV at t6 = PV(5%,20,-50000) = $623,111 SO PV at t0 = $623,111/(1+10%/2)^(6*2) = $346,972 So Lump sum today is sum of 1+2+3 above = 55684+329081+346972 = $731,736 So Jack needs to deposit $731,736 today
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