Question

Suppose you currently have $5,000 in your savings account, and your bank pays interest at a rate of 0.5% per month. If you n how much will you have in the account in 5 years? In 5 years' time, you will have $ in the account. (Round to the nearest cent.)

Answer 1

We are given the following information:

PV	5000
r = annual interest rate	0.5 x 12 = 6.00%
n	5
frequency (monthly compounding)	12

We need to solve the following equation to arrive at the required FV

FV = PV X (1+ -) frequencyxn frequency

FV = 5000 x (1 + 0.06, 12x5

FV = 6744.25

So in 5 years, the account will have $6744.25 in it

Lets verify the same with a compounding schedule:

Closing balance = Opening balance + Interest Month Opening Balance = | Interest = 0.5% x opening balance Previous month's closing balance 0 $ 5,000.00 1 $ 5,000.00 0.5% x 5000 = $ 25.00 2 $ 5,025.00 0.5% x 5025 = $ 25.13 3 $ 5,050.13 0.5% x 5050.125 = $ 25.25 4 $ 5,075.38 0.5% x 5075.375625 = $ 25.38 5 $ 5,100.75 0.5% x 5100.752503125 = $ 25.50 6 $ 5,126.26 0.5% x 5126.25626564062 = $ 25.63 7$ 5,151.89 0.5% x 5151.88754696883 = $ 25.76 8 $ 5,177.65 0.5% x 5177.64698470367 = $ 25.89 9 $ 5,203.54 0.5% x 5203.53521962719 = $ 26.02 10 $ 5,229.55 0.5% x 5229.55289572533 = $ 26.15 11 $ 5,255.70 0.5% x 5255.70066020395 = $ 26.28 12 $ 5,281.98 0.5% x 5281.97916350497 = $ 26.41 13 $ 5,308.39 0.5% x 5308.3890593225 = $26.54 14 $ 5,334.93 0.5% x 5334.93100461911 = $26.67 15 $ 5,361.61 0.5% x 5361.6056596422 = $ 26.81 16 $ 5,388.41 0.5% x 5388.41368794042 = $26.94 17 $ 5,415.36 0.5% x 5415.35575638012 = $ 27.08 18 $ 5,442.43 0.5% x 5442.43253516202 = $ 27.21 19 $ 5,469.64 0.5% x 5469.64469783783 = $ 27.35 20 $ 5,496.99 0.5% x 5496.99292132702 = $ 27.48 21 $ 5,524.48 0.5% x 5524.47788593365 = $ 27.62 22 $ 5,552.10 0.5% x 5552.10027536332 = $ 27.76 23 $ 5,579.86 0.5% x 5579.86077674014 = $ 27.90 24 $ 5,607.76 0.5% x 5607.76008062384 = $ 28.04 25 $ 5,635.80 0.5% x 5635.79888102696 = $ 28.18 26 $ 5,663.98 0.5% x 5663.97787543209 = $ 28.32 27 $ 5,692.30 0.5% x 5692.29776480925 = $ 28.46 28 $ 5,720.76 0.5% x 5720.7592536333 = $ 28.60 29 $ 5,749.36 0.5% x 5749.36304990147 = $ 28.75 30 $ 5,778.11 0.5% x 5778.10986515097 = $ 28.89 31 $ 5,807.00 0.5% x 5807.00041447673 = $ 29.04 32 $ 5,836.04 0.5% x 5836.03541654911 = $ 29.18 33 $ 5,865.22 0.5% x 5865.21559363186 = $ 29.33 34 $ 5,894.54 0.5% x 5894.54167160002 = $ 29.47 35 $ 5,924.01 0.5% x 5924.01437995802 = $ 29.62 36 $ 5,953.63 0.5% x 5953.63445185781 = $ 29.77 37 $ 5,983.40 0.5% x 5983.4026241171 = $29.92 38 $ 6,013.32 0.5% x 6013.31963723768 = $ 30.07 39 $ 6,043.39 0.5% x 6043.38623542387 = $ 30.22 40 $ 6,073.60 0.5% x 6073.60316660099 = $ 30.37 41 $ 6,103.97 0.5% x 6103.97118243399 = $ 30.52 42 $ 6,134.49 0.5% x 6134.49103834616 = $ 30.67 43 $ 6,165.16 0.5% x 6165.1634935379 = $ 30.83 44 $ 6,195.99 0.5% x 6195.98931100558 = $ 30.98 45 $ 6,226.97 0.5% x 6226.96925756061 = $ 31.13 46 $ 6,258.10 0.5% x 6258.10410384842 = $ 31.29 471 $ 6,289.39 0.5% x 6289.39462436766 = $ 31.45 48 $ 6,320.84 0.5% x 6320.8415974895 = $ 31.60 49 $ 6,352.45 0.5% x 6352.44580547694 = $ 31.76 50 $ 6,384.21 0.5% x 6384.20803450433 = $ 31.92 51 $ 6,416.13 0.5% x 6416.12907467685 = $ 32.08 52 $ 6,448.21 0.5% x 6448.20972005023 = $ 32.24 53 $ 6,480.45 0.5% x 6480.45076865048 = $ 32.40 54 $ 6,512.85 0.5% x 6512.85302249374 = $ 32.56 55 $ 6,545.42 0.5% x 6545.41728760621 = $ 32.73 56 $ 6,578.14 0.5% x 6578.14437404424 = $ 32.89 57 $ 6,611.04 0.5% x 6611.03509591446 = $ 33.06 58 $ 6,644.09 0.5% x 6644.09027139403 = $ 33.22 59 $ 6,677.31 0.5% x 6677.310722751 = $33.39 60 $ 6,710.70 0.5% x 6710.69727636476 = $ 33.55 $ 5,000.00 5000 + 25 = $ 5,025.00 5025 + 25.125 = $ 5,050.13 5050.125 + 25.250625 = $ 5,075.38 5075.375625 + 25.376878125 = $ 5,100.75 5100.752503125 + 25.503762515625 = | $ 5,126.26 5126.25626564062 +25.6312813282031 = $ 5,151.89 5151.88754696883 +25.7594377348441 = $ 5,177.65 5177.64698470367 +25.8882349235184 = | $ 5,203.54 5203.53521962719 + 26.017676098136 = $ 5,229.55 5229.55289572533 +26.1477644786266 = $ 5,255.70 5255.70066020395 + 26.2785033010198 = | $ 5,281.98 5281.97916350497 +26.4098958175249 = $ 5,308.39 5308.3890593225 +26.5419452966125 = $ 5,334.93 5334.93100461911 + 26.6746550230955 = $ 5,361.61 5361.6056596422 + 26.808028298211 = $5,388.41 5388.41368794042 + 26.9420684397021 = $5,415.36 5415.35575638012 + 27.0767787819006 = $ 5,442.43 5442.43253516202 + 27.2121626758101 = $ 5,469.64 5469.64469783783 + 27.3482234891891 = $ 5,496.99 5496.99292132702 + 27.4849646066351 = | $ 5,524.48 5524.47788593365 + 27.6223894296683 = $ 5,552.10 5552.10027536332 +27.7605013768166 = $ 5,579.86 5579.86077674014 + 27.8993038837007 = $ 5,607.76 5607.76008062384 + 28.0388004031192 = $ 5,635.80 5635.79888102696 +28.1789944051348 = $ 5,663.98 5663.97787543209 + 28.3198893771605 = $ 5,692.30 5692.29776480925 + 28.4614888240463 = $ 5,720.76 5720.7592536333 +28.6037962681665 = $ 5,749.36 5749.36304990147 +28.7468152495073 = $ 5,778.11 5778.10986515097 +28.8905493257549 = $ 5,807.00 5807.00041447673 + 29.0350020723836 = $ 5,836.04 5836.03541654911 + 29.1801770827456 = $ 5,865.22 5865.21559363186 +29.3260779681593 = $ 5,894.54 5894.54167160002 +29.4727083580001 = $ 5,924.01 5924.01437995802 + 29.6200718997901 = $ 5,953.63 5953.63445185781 +29.768172259289 = $ 5,983.40 5983.4026241171 +29.9170131205855 = $ 6,013.32 6013.31963723768 + 30.0665981861884 = $ 6,043.39 6043.38623542387 +30.2169311771193 = $ 6,073.60 6073.60316660099 + 30.3680158330049 = $ 6,103.97 6103.97118243399 + 30.51985591217 = $ 6,134.49 6134.49103834616 + 30.6724551917308 = $ 6,165.16 6165.1634935379 + 30.8258174676895 = $ 6,195.99 6195.98931100558 + 30.9799465550279 = $ 6,226.97 6226.96925756061 + 31.1348462878031 = | $ 6.258.10 6258.10410384842 + 31.2905205192421 = $ 6,289.39 6289.39462436766 +31.4469731218383 = $ 6,320.84 6320.8415974895 + 31.6042079874475 = $ 6,352.45 6352.44580547694 + 31.7622290273847 = $ 6,384.21 6384.20803450433 +31.9210401725216 = $ 6,416.13 6416.12907467685 + 32.0806453733843 = $ 6,448.21 6448.20972005023 +32.2410486002512 = $ 6,480.45 6480.45076865048 + 32.4022538432524 = $ 6,512.85 6512.85302249374 + 32.5642651124687 = $ 6,545.42 6545.41728760621 + 32.727086438031 = $ 6,578.14 6578.14437404424 +32.8907218702212 = $ 6,611.04 6611.03509591446 +33.0551754795723 = $ 6,644.09 6644.09027139403 +33.2204513569702 = $ 6,677.31 6677.310722751 +33.386553613755 = $ 6,710.70 6710.69727636476 +33.5534863818238 = $ 6,744.25