A loan of $2000 at 12% is compunded monthly for two years. Find the future value

Question

A loan of $2000 at 12% is compunded monthly for two years. Find the future value and compound interest. Use the $1.00 future value table or the future value and compund interest

page 2 of the future value table. uture value or Compound Amount of $1.00 Rate per period ods 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3 50% 4.00% 4.50% 5.00% 5.50% 1.00500 1.01000 1.01500 1.02000 1.02500 1.03000 1.0 3500 1.04000 1.04500 1. 05000 1.05500 2 1.01003 1.02010 1.03023 1.04040 1.05063 1.06090 1.07 123 1.08 160 1 0920 1 10250 1 30 3 1.01508 1.03030 1.04568 1.06121 1.07689 1.09273 1.10872 1.12486 1.14117 1.15763 1.17424 4 1.02015 1.04060 1.06136 1.08243 1.10381 1.12551 1.1 4752 1.1 1, 19252 1 21551 1 23882 5 1.02525 1.05101 1.07728 1.10408 1.13141 1.15927 1 18769 1.21665 1 24618 1 27628 1.30696 6 1.03038 1.06152 1.09344 1.12616 1.15969 1.19405 1.229 26 1.265 32 1 30226 1.34010 1.37884 7 1.03553 1.07214 1.10984 1.14869 1.18869 1.22 987 1 27228 1 31593 1.36086 140710 1,45468 8 1.04071 1.08286 1.12649 1.17166 1.21840 1.26677 1.3 1681 1. 36857 1 42210 1.47746 1.53469 9 1.04591 1.09369 1.14339 1.19509 1 24886 1 30477 1.36290 1.42331 1.48610 1 55133 1.61909 10 1.05114 1.10462 1.16054 1.21899 1.28008 1.34392 1.41060 1.48024 1 55 297 1 62 89 1.708 14 11 1.05640 1.11567 1.17795 1.24337 1.31209 1.38423 1,45997 1,53945 1,62285 1,710 34 1 80209 1.06168 1.12683 1.19562 1.26824 1 34489 1.42576 1 51107 1.60103 1 69588 1 79586 190121 12 13 1.06699 1.13809 1.21355 1.29361 1.37851 1.46853 1.56 396 1 66507 1. 77220 1 88565 2.00577 14 1.07232 1.14947 1.23176 1.31948 1.41297 1 51 259 1,6 1869 1, 73168 1 85194 1 9799 2.1 60 15 1.07768 1.16097 1.25023 1.34587 144830 1 55797 1.67535 1 800 94 1 93528 2.0789 2.2 48 16 1.08307 1.17258 1.26899 1.37279 1 48451 1 60471 1,73 399 1 87 298 202237 2 18 287 2, 35526 17 1.08849 1.18430 1.28802 1 40024 1.52162 1.65285 1.79468 1.94790 2.11338 2.29202 2 48480 18 1.09393 1.19615 1.30734 1.42825 1.55966 1,7024 1 85749 2.02582 2 2084 2 40662 2 6214 19 1.09940 1.20811 1.32695 1.45681 1 59865 1.75351 1 92250 2.10685 2.30 786 2 2695 2.76565 1 98979 2-19112 24 71 2 65 330 2 91776 20 1.10490 1.22019 1.34686 1.48595 1 63862 1 80611 21 1.11042 1.23239 1.36706 1 51567 1 67958 1 86029 2.05943 2.27877 2.52024 278596 3.07823 22 1.11597 1.24472 1.38756 1.54598 1.72157 1.91610 2. 131 51 2369 92 2.6 365 2.92526 324 754 1.12155 1.25716 1.40838 1.57690 1.76461 1 97359 2 20611 2 46472 2. 521 307152 3 261 24 12716 1.26973 1,42950 1 60844 1.80873 2.03279 2.28333 2.56330 2.87601 3 25 1.13280 1 28243 1.45095 1.64061 1.85394 2.09 378 2 36324 266584 3.00543 338635 3.81339 26 1.13846 1.29526 1,47271 1,67342 1.90029 2. 5659 2.445 96 2.7 7247 3.1 4068 3 55567 402313 27 1.14415 1.30821 1.49480 1.70689 1.94780 2 22129 2.53157 2.88337 3.28201 3.73346 4 24440 174102 199650 228793 262017 299 87o 342970 2013 28 1.32129 151722 3.58404 4.11614 4.724 12 29 1.15562 1.33450 1.53998 1.77584 2.04641 2 35657 2.7 1188 3 11865 30 1.16140 1.34785 1 56308 1811 36 2.09757 2 427 26 2 80679 324 340 3 4.32194 498395 4.50% 5.00% 5.50% Periods 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3-50% 4.00% Rate per period Table shows future value (F) of $1.00 compounded for N periods at R rate per period

Explanation / Answer

As the compounding has been done at a monthly rate of 12% per annum, therefore the effective monthly interest rate would be:

12 / 12 = 1% per month as there are 12 months in a year.

Now in 2 years, there will be 2*12 = 24 period of 1 month,

Therefore for 24 periods and interest rate of 1%, the future value of $1 from the given table would be:

FV = $1.26973 as obtained from the above given table.

Therefore the future value of a loan of $2000 would be:

FV = 2000* 1.26973 = 2539.46

Therefore the compound interest in 2 years would be:

= 2539.46 - 2000 = $539.46

Therefore final answers are:

Future value = $2539.46

Compound interest = $539.46

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