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lebronjames1604
07.03.2020 •
Mathematics
Suppose that a sum S0 is invested at an annual rate of return r compounded continuously. (a) Find the time T required for the original sum to double in value as a function of r. (b) Determine T if r = 7%. (c) Find the return rate that must be achieved if the initial investment is to double in 8 years.Please explain!
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Ответ:
a) T = ln2/ln[(100+r)/100]
b) 10.2 years (3 sf)
c) 9.05% (3 sf)
Step-by-step explanation:
r% return: amount is (100+r)%
S = S0 × [(100+r)/100]^T
S = 2S0
2S0 = S0×[(100+r)/100]^T
2 = [(100+r)/100]^T
ln(2) = T ln[(100+r)/100]
T = ln2/ln[(100+r)/100]
b) r = 7
T = ln2/ln[(100+7)/100]
T = ln2/ln1.07
T = 10.24476837 years
T = 10.2 years (3 sf)
c) T = 8
8 = ln2/ln[(100+r)/100]
ln[(100+r)/100] = ln2/8
1 + r/100 = 1.090507733
r/100 = 0.090507733
r = 9.0507733%
r = 9.05% (3 sf)
Ответ:
(20, 80)
(80, 20)
(80, 0)
Step-by-step explanation:
Got it right on Edg 2020!!