Derek will deposit $2,185.00 per year for 14.00 years into an account that earns 8.00%. Assuming the first deposit is made 6.00 years from today, how much will be in the account 32.00 years from today?
Derek will deposit $5,800.00 per year for 27.00 years into an account that earns 16.00%, The first deposit is made next year. How much will be in the account 37.00 years from today?
Derek will deposit $1,404.00 per year for 16.00 years into an account that earns 13.00%. The first deposit is made today. How much will be in the account 16.0 years from today?
Derek will deposit $6,877.00 per year for 12.00 years into an account that earns 14.00%, The first deposit is made next year. He has $19,281.00 in his account today. How much will be in the account 46.00 years from today?
Derek will deposit $8,190.00 per year for 23.00 years into an account that earns 4.00%, The first deposit is made next year. How much will be in the account 40.00 years from today?
Answer Format: Currency: Round to: 2 decimal places
i)
Formula for FV of annuity is:
FV = P x [(1+r) n – 1/r]
P = Periodic cash flow = $ 2,185
r = Rate per period = 8 % or 0.08 p.a.
n = Numbers of periods = 14
FV = $ 2,185 x [(1+0.08)14 – 1/0.08]
= $ 2,185 x [(1.08)14 – 1/0.08]
= $ 2,185 x [(2.937193624258 – 1)/0.08]
= $ 2,185 x (1.937193624258/0.08)
= $ 2,185 x 24.21492030322
= $ 52,909.600862537 or $ 52,909.60
Fund size in year 14 is $ 52,909.60, Future value of this fund in year 32 can be computed as
FV = PV x (1+r) n
n = Numbers of periods = 32 – 14 – 6 = 12
FV = $ 52,909.600862537 x (1+0.08)12
= $ 52,909.600862537 x (1.08)12
= $ 52,909.600862537 x 2.518170116819
= $ 133,235.375784861 or $ 133,235.38
There will be $ 133,235.38 in the account 32 years from today.
ii)
Formula for FV of annuity is:
FV = P x [(1+r) n – 1/r]
P = Periodic cash flow = $ 5,800
r = Rate per period = 16 % or 0.16 p.a.
n = Numbers of periods = 27
FV = $ 5,800 x [(1+0.16)27 – 1/0.16]
= $ 5,800 x [(1.16)27 – 1/0.16]
= $ 5,800 x [(55.000382414179– 1)/0.16]
= $ 5,800 x (54.000382414179/0.16)
= $ 5,800 x 337.50239008862
= $ 1,957,513.8625140 or $ 1,957,513.86
Fund size in year 27 is $ 1,957,513.86, Future value of this fund in year 37 can be computed as
FV = PV x (1+r) n
n = Numbers of periods = 37 – 27 =10
FV = $ 1,957,513.8625140 x (1+0.16)10
= $ 1,957,513.8625140 x (1.16)10
= $ 1,957,513.8625140 x 4.411435078650
= $ 8635445.32003774 or $ 8,635,445.32
There will be $ 8,635,445.32 in the account 37 years from today.
iii)
Formula for FV of annuity due is:
FV = (1+r) x P x [(1+r) n – 1/r]
P = Periodic cash flow = $ 1,404
r = Rate per period = 13 % or 0.13 p.a.
n = Numbers of periods = 16
FV = (1+0.13) x $ 1,404 x [(1+0.13) 16 – 1/0.13]
= (1.13) x $ 1,404 x [(1.13) 16 – 1/0.13]
= $ 1,586.52 x [(7.067325526798 – 1)/0.13]
= $ 1,586.52 x (6.067325526798/0.13)
= $ 1,586.52 x 46.67173482152
= $ 74,045.6407290 or $ 74,045.64
There will be $ 74,045.64 in the account 16 years from today.
iv)
FV of annuity in year 12:
FV = P x [(1+r) n – 1/r]
P = Periodic cash flow = $ 6,877
r = Rate per period = 14 % or 0.14 p.a.
n = Numbers of periods = 12
FV = $ 6,877 x [(1+0.14)12 – 1/0.14]
= $ 6,877 x [(1.14)12 – 1/0.14]
= $ 6,877 x [(4.817904819829 – 1)/0.14]
= $ 6,877 x (3.817904819829/0.14)
= $ 6,877 x 27.27074871306
= $ 187,540.938899718 or $ 187,540.94
FV of $ 187,540.94 in year 46:
FV = $ 187,540.938899718 x (1+0.14) (46 – 12)
= $ 187,540.938899718 x (1.14) 34
= $ 187,540.938899718 x 86.05278799290
= $ 16,138,420.65512670
FV of single sum $ 19,281 in year 46:
FV = $ 19,281 x (1+0.14)46
= $ 19,281 x (1.14)46
= $ 19,281 x 414.594142030667
= $ 7,993,789.65249329
Total fund size in year 46 = $ 16,138,420.65512670 + $ 7,993,789.65249329
= $ 24,132,210.30761990 or $ 24,132,210.31
There will be $ 24,132,210.31 in the account 46 years from today.
v)
FV of annuity in year 23:
FV = P x [(1+r) n – 1/r]
P = Periodic cash flow = $ 8,190
r = Rate per period = 4 % or 0.04 p.a.
n = Numbers of periods = 23
FV = $ 8,190 x [(1+0.04)23 – 1/0.04]
= $ 8,190 x [(1.04)23 – 1/0.04]
= $ 8,190 x [(2.464715543165 – 1)/0.04]
= $ 8,190 x (1.464715543165/0.04)
= $ 8,190 x 36.61788857913
= $ 299,900.50746306 or $ 299,900.51
FV of $ 299,900.51 in year 40:
FV = $ 299,900.50746306 x (1+0.04) (40 – 23)
= $ 299,900.50746306 x (1.04) 17
= $ 299,900.50746306 x 1.94790049555628
= $ 584,176.347104882 or $ 584,176.35
There will be $ 584,176.35 in the account 40 years from today.
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