You will receive $50,165 per year for the next 15 years from your annuity plan.
ID: 2759589 • Letter: Y
Question
You will receive $50,165 per year for the next 15 years from your annuity plan. What is the present value of the annuity payments if your opportunity cost is 9%?
What is the present value of $10,863 that you will receive in 6 years if your opportunity cost of money is 6% per year?
If you lend $1,498 today and reveive $2,021 in 9 years, what is the interest rate you are charging? Write your answer in decimals (e.g., write in .0852 for 8.52%).
If you took out an auto loan of $26,209 at the interest rate of 9% p.a., for 5 years, how much will be your 'monthly' payment?
If you save and invest $201 a month for the next 11 years for your child, how much money would you have in your child's 529 plan in 11 years if the plan's average return is 11% p.a.?
Explanation / Answer
1)
K = N
Present value of annuity = [(Annuity payment)/(1 + Required rate of return)^k]
k=1
K = 15
Present value of annuity = [(50165)/(1 +9/100)^k]
k=1
=404364.43
2) PV = FV/(1+r)^n = 10863/(1+0.06)^6
=7657.986
3) PV = FV/(1+r)^n
1498=2021/(1+r)^9
R = 3.38%
4)
Where
Interest paid = Beginning balance * monthly interest rate
Principal = Monthly payment – interest paid
Ending balance = beginning balance – principal paid
Beginning balance = previous year ending balance
Monthly rate(M)= annual rate/12 0.75% Monthly payment= 544.0557321 Month Beginning balance (A) Ending balance Interest = M*A Principal paid Ending balance 1 26209 544.0557321 196.5675 347.4882321 25861.51177 2 25861.51177 544.0557321 193.9613383 350.0943939 25511.41737 3 25511.41737 544.0557321 191.3356303 352.7201018 25158.69727 4 25158.69727 544.0557321 188.6902295 355.3655026 24803.33177 5 24803.33177 544.0557321 186.0249883 358.0307439 24445.30103 6 24445.30103 544.0557321 183.3397577 360.7159744 24084.58505 7 24084.58505 544.0557321 180.6343879 363.4213442 23721.16371 8 23721.16371 544.0557321 177.9087278 366.1470043 23355.0167 9 23355.0167 544.0557321 175.1626253 368.8931069 22986.1236 10 22986.1236 544.0557321 172.395927 371.6598052 22614.46379 11 22614.46379 544.0557321 169.6084784 374.4472537 22240.01654 12 22240.01654 544.0557321 166.800124 377.2556081 21862.76093 13 21862.76093 544.0557321 163.970707 380.0850252 21482.6759 14 21482.6759 544.0557321 161.1200693 382.9356628 21099.74024 15 21099.74024 544.0557321 158.2480518 385.8076803 20713.93256 16 20713.93256 544.0557321 155.3544942 388.7012379 20325.23132 17 20325.23132 544.0557321 152.4392349 391.6164972 19933.61483 18 19933.61483 544.0557321 149.5021112 394.5536209 19539.0612 19 19539.0612 544.0557321 146.542959 397.5127731 19141.54843 20 19141.54843 544.0557321 143.5616132 400.4941189 18741.05431 21 18741.05431 544.0557321 140.5579073 403.4978248 18337.55649 22 18337.55649 544.0557321 137.5316737 406.5240585 17931.03243 23 17931.03243 544.0557321 134.4827432 409.5729889 17521.45944 24 17521.45944 544.0557321 131.4109458 412.6447863 17108.81465 25 17108.81465 544.0557321 128.3161099 415.7396222 16693.07503 26 16693.07503 544.0557321 125.1980627 418.8576694 16274.21736 27 16274.21736 544.0557321 122.0566302 421.9991019 15852.21826 28 15852.21826 544.0557321 118.891637 425.1640952 15427.05417 29 15427.05417 544.0557321 115.7029062 428.3528259 14998.70134 30 14998.70134 544.0557321 112.49026 431.5654721 14567.13587 31 14567.13587 544.0557321 109.253519 434.8022131 14132.33365 32 14132.33365 544.0557321 105.9925024 438.0632297 13694.27042 33 13694.27042 544.0557321 102.7070282 441.3487039 13252.92172 34 13252.92172 544.0557321 99.3969129 444.6588192 12808.2629 35 12808.2629 544.0557321 96.06197176 447.9937604 12360.26914 36 12360.26914 544.0557321 92.70201856 451.3537136 11908.91543 37 11908.91543 544.0557321 89.31686571 454.7388664 11454.17656 38 11454.17656 544.0557321 85.90632421 458.1494079 10996.02715 39 10996.02715 544.0557321 82.47020365 461.5855285 10534.44162 40 10534.44162 544.0557321 79.00831218 465.0474199 10069.3942 41 10069.3942 544.0557321 75.52045654 468.5352756 9600.858929 42 9600.858929 544.0557321 72.00644197 472.0492902 9128.809639 43 9128.809639 544.0557321 68.46607229 475.5896598 8653.219979 44 8653.219979 544.0557321 64.89914984 479.1565823 8174.063397 45 8174.063397 544.0557321 61.30547548 482.7502567 7691.31314 46 7691.31314 544.0557321 57.68484855 486.3708836 7204.942257 47 7204.942257 544.0557321 54.03706692 490.0186652 6714.923591 48 6714.923591 544.0557321 50.36192694 493.6938052 6221.229786 49 6221.229786 544.0557321 46.6592234 497.3965087 5723.833277 50 5723.833277 544.0557321 42.92874958 501.1269825 5222.706295 51 5222.706295 544.0557321 39.17029721 504.8854349 4717.82086 52 4717.82086 544.0557321 35.38365645 508.6720757 4209.148784 53 4209.148784 544.0557321 31.56861588 512.4871162 3696.661668 54 3696.661668 544.0557321 27.72496251 516.3307696 3180.330898 55 3180.330898 544.0557321 23.85248174 520.2032504 2660.127648 56 2660.127648 544.0557321 19.95095736 524.1047748 2136.022873 57 2136.022873 544.0557321 16.02017155 528.0355606 1607.987313 58 1607.987313 544.0557321 12.05990485 531.9958273 1075.991485 59 1075.991485 544.0557321 8.069936141 535.985796 540.0056895 60 540.0056895 544.0557321 4.050042671 540.0056895 1.81899E-12Related Questions
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