Question

2. Monthly vs. Yearly Sayings You are able to save $200 a month ($2,400 per year) You can invest in a CD account with 4.5% annual return or an equity fund with an expected annual return of 8%. Assume that the expected annual return of the equity fund materializes, what will be your savings in 35 years for both investment opportunities? a) If you make annual savings of $2,400 to the CD. (assume annual compounding) b) If you make annual savings of $2,400 to the equity fund. (assume annual compounding) c) If you make monthly savings of $200 to the CD. (assume annual compounding) d) If you make monthly savings of $200 to the equity. (assume annual compounding) e) If you make monthly savings of $200 to the CD. (assume monthly compounding) f) If you make monthly savings of $200 to the equity. (assume monthly compounding)

Answer 1

future Amount of an annuity & A ( 1 ) - 1) 1 / (a) where A a annuity installment = $ 2400 4051/9 - Your = 0.045 n = 35 years by putting the values in the above forumlar we get a - 35 = $2400 (70.045) -1. 0.045 z $ 53 333.33 [1.045 17-ci fame (le cour) -1

Ilona 35 (0.0334) & (6169 az Antily (1-169) é 14076 by putting the values in o, we get . z 30,0w |(14.76 )-1] - $ 412,50/- = so If monthly savings all done of $ 200 each month, but the interest is compounded annually, not monthly, then there will be seune future value of instalments made. do, We can say that there will be no change in future value is calculated in (a) because the interest is compouded I annually. So savings in 38 years will se $ 195252/- If monthly savings of $ 200 all done in equity fund and the suscrest is compounded annually, then the future value of enigs in 35 years will be same as in (6) il 2 $ 412 8w17

Ilona 35 (0.0334) = 1.168 . az Antily (1-169) ¿ 14.76 by putting the values in ce we get . 230,0w |(14.76 ) - 1] a $ 412 80 - Solat If monthly savings all done of $ 200 each month, but the interest is compounded annually, not monthly, then there will be same future value of instalmeints made. Oo, We can say that there will be no change in future value is calculated in (a), because the interest is compouded annually: ST . I So savings in 38 years will se $ 1952591- T If monthly savings of $ 200 all done in epuity fund and the duserest is compounded annually, then the future value of fennes in 8 years will be same as in (6) z $ 41 28W / 9

PAGE NU Monthly compounety here A = $200 per month to bro45/12 = 0.00375 monthly ta 350/2 a 420 months By putting the values in formula, we get future value = $200 (A+0.00375) - 1 0.00375 420 = 58333 61.00375)2° -1 sis I let a=(1.00375 920 is log both sides, we get loga a 450 top 100375 on a 420 (0.00160) = 0.672 ł z Ant6-672) = 4.699 By putting the value of nim , we get = 53333 [ 4.699-17 - $ 197976.36 = $197979 (ES Here A = $ 200 per month ro a 0.08/12 0.0067 ta 35x12 a 420 months By putting the values in formula we get &

4204 $ Leo 920 daki It 000067) - - 0.0067 = $30,000 F (1.0067) 920 I r- ci det n = (160o67) " both sides len ² 420 by 160o 67 in a 420 (0.00290) = rets nz Antily (1.28) n = 16.52 By putting the value of u in cig we get $30000 [1652 - 1] = 20000 (15.52) = $ 46560 /