using the annuity formula: F = (Pn/r)[(1 + (r/n)) nt+1 1] where: F is the future
ID: 2426941 • Letter: U
Question
using the annuity formula:
F = (Pn/r)[(1 + (r/n))nt+1 1]
where:
F is the future value of ALL of the investments/loans, including interest.
• P is the principal amount invested or paid at the beginning of each period.
• r is the annual interest rate, written as a decimal (ex: 6% =.06).
• n is the number of times that interest is compounded per year.
• t is the number of years the money is invested or borrowed.
Suppose you invest P at the beginning of each month in a retirement account in hopes to save $600,000 for retirement at the age of 65. For both the annual rates r = 3.2% and r = 8.05%, compounded monthly, find the amount of money you will need to invest per month:
A. if you start this process as soon as you turn 23 (so you invest for 42 years total).
B. if you start this process as soon as you turn 30 (so you invest for 35 years total).
C. if you start this process as soon as you turn 40 (so you invest for 25 years total).
Explanation / Answer
Answer a :
If Current age is 23
return = 3.2%
FV = C * {(1+i)n-1/i}
600000 = C * {(1+0.032)42-1/0.032}
C = 6754.4
Return = 8.05%
FV = C * {(1+i)n-1/i}
600000 = C * {(1+0.0805)42-1/0.0805}
C = 1799.90
Answer B:
If Current age is 30
return = 3.2%
FV = C * {(1+i)n-1/i}
600000 = C * {(1+0.032)35-1/0.032}
C = 9249
Return = 8.05%
FV = C * {(1+i)n-1/i}
600000 = C * {(1+0.0805)35-1/0.0805}
C = 3186.9
Answer C :-
If Current age is 40
return = 3.2%
FV = C * {(1+i)n-1/i}
600000 = C * {(1+0.032)25-1/0.032}
C = 15532.10
Return = 8.05%
FV = C * {(1+i)n-1/i}
600000 = C * {(1+0.0805)25-1/0.0805}
C = 7540.5
Check
Age Year Investment Opening Intt rate Intt Closing 40 1 7540.5 7540.5 8.05% 607.0103 8147.51 41 2 7540.5 15688.01 8.05% 1262.885 16950.9 42 3 7540.5 24491.4 8.05% 1971.557 26462.95 43 4 7540.5 34003.45 8.05% 2737.278 36740.73 44 5 7540.5 44281.23 8.05% 3564.639 47845.87 45 6 7540.5 55386.37 8.05% 4458.603 59844.97 46 7 7540.5 67385.47 8.05% 5424.531 72810 47 8 7540.5 80350.5 8.05% 6468.215 86818.72 48 9 7540.5 94359.22 8.05% 7595.917 101955.1 49 10 7540.5 109495.6 8.05% 8814.399 118310 50 11 7540.5 125850.5 8.05% 10130.97 135981.5 51 12 7540.5 143522 8.05% 11553.52 155075.5 52 13 7540.5 162616 8.05% 13090.59 175706.6 53 14 7540.5 183247.1 8.05% 14751.39 197998.5 54 15 7540.5 205539 8.05% 16545.89 222084.9 55 16 7540.5 229625.4 8.05% 18484.84 248110.2 56 17 7540.5 255650.7 8.05% 20579.88 276230.6 57 18 7540.5 283771.1 8.05% 22843.58 306614.7 58 19 7540.5 314155.2 8.05% 25289.49 339444.7 59 20 7540.5 346985.2 8.05% 27932.31 374917.5 60 21 7540.5 382458 8.05% 30787.87 413245.9 61 22 7540.5 420786.4 8.05% 33873.3 454659.7 62 23 7540.5 462200.2 8.05% 37207.11 499407.3 63 24 7540.5 506947.8 8.05% 40809.3 547757.1 64 25 7540.5 555297.6 8.05% 44701.46 599999 65Related Questions
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