Question

Problem 4-59 Calculating Annuity Values Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with a retirement income of $26,000 per month for 20 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $340,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $1,100,000 to his nephew Frodo. He can afford to save $2.500 per month for the next 10 years. If he can earn an EAR of 10 percent before he retires and an EAR of 7 percent after he retires, how much will he have to save each month in Years 11 through 30? (Do not round Intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Monthly savings SC

Answer 1

Future value calculation for Monthly contribution of $ 2500 Time 10 Years EAR 10% Monthly Contribution $ 2,500 Yearly contribution would be (2500*12) $ 30,000 Future value for yearly contribution of $30000 Year wa0008 30000 30000 30000 30000 30000 30000 30000 30000 30000 30000 1.1 1.21 1.331 1.4641 1.61051 1.771561 1.9487171 2.14358881 2.357947691 2.59374246 33,000.00 36,300.00 39,930.00 43,923.00 48,315.30 53,146.83 58,461.51 64,307.66 70,738.43 77,812.27 5,25,935.01 $ avaiable at the end of 10th year Cabin Purchased on 10th year Remaingn $ at end of 10 th year FV value of $ 185935.01 or 5,25,935.01 3,40,000.00 1,85,935.01 12,49,483.28 6.72

PV value of retirement income of $ 26000 per month for 20 years at the 11th year and inheritence of 11,00,000 at 50th 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 3,12,000.00 11,00,000.00 PV at 30th Year 3,12,000 1.07 0.934579442,91,589 1.1449 0.87343873 2,72,513 1.225043 0.81629788 2,54,685 1.31079601 0.76289521 2,38,023 1.402551731 0.712986182,22,452 1.500730352 0.666342222,07,899 1.605781476 0.62274974 1,94,298 1.71818618 0.5820091 1,81,587 1.838459212 0.54393374 1,69,707 1.967151357 0.50834929 1,58,605 2.104851952 0.4750928 1,48,229 2.252191589 0.44401196 1,38,532 2.409845 0.41496445 1,29,469 2.57853415 0.38781724 1,20,999 2.759031541 0.36244602 1,13,083 2.952163749 0.3387346 1,05,685 3.158815211 0.31657439 98,771 3.379932276 0.29586392 92,310 3.616527535 0.27650833 86,271 3.869684462 0.258419 2,84,261 38,20,967 12,49,483 $ avaiable Remaining $ amount to be saved 25,71,483

For having 25,71,483, the person needs to invest 21,781 per month from the 11th year till 30th year (Note - $ 21,781 is calculated through EMI formula) EMI = (P x R x (1+R)^N]/((1+R)^N-1