How is frequent compounding related to the number e if we change the interest rate? Walue of a dollar after daily compounding for one year Value of a dollar after hourly compounding for one year e' continuously Interest rate To seven decimal places 0.03 1.0304532 1.0304544 1.0304545 0.05 1.051267 1.051270 1.0512710 0.08 1.083277 1.083286 1.0832870 4-5 digit accura cey (a) What is the point being made by this table? (b) Based on this table, for large values of n, (1+:)" -_er. So a dollar compounded continuously at 3% will grow to e00 1.030454534 at the end of one year. If you invest one million dollars compounded continuously at 3%, how much will you have at the end of one year? 1.030454, 534 236 454,53 (c) If you invest $10,000 in an account that pays 8% compounded continuously, how much will you have at the end of the year? 16,832.87 Generalization: For large values of n, (1+4)" - _e" continuously, the banking formula is A= P(1+)" becomes So if an investment is compounded A=Pert
How is frequent compounding related to the number e if we change the interest rate? Walue of a dollar after daily compounding for one year Value of a dollar after hourly compounding for one year e' continuously Interest rate To seven decimal places 0.03 1.0304532 1.0304544 1.0304545 0.05 1.051267 1.051270 1.0512710 0.08 1.083277 1.083286 1.0832870 4-5 digit accura cey (a) What is the point being made by this table? (b) Based on this table, for large values of n, (1+:)" -_er. So a dollar compounded continuously at 3% will grow to e00 1.030454534 at the end of one year. If you invest one million dollars compounded continuously at 3%, how much will you have at the end of one year? 1.030454, 534 236 454,53 (c) If you invest $10,000 in an account that pays 8% compounded continuously, how much will you have at the end of the year? 16,832.87 Generalization: For large values of n, (1+4)" - _e" continuously, the banking formula is A= P(1+)" becomes So if an investment is compounded A=Pert
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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can you help me with letter A
Transcribed Image Text:How is frequent compounding related to the number e if we change the interest rate?
Value of a dollar after Value of a dollar after
e"
hourly compounding
continuously
daily compounding
for one year
Interest rate
for one year
To seven decimal places
0.03
1.0304532
1.0304544
1.0304545
0.05
1.051267
1.051270
1.0512710
0.08
1.083277
1.083286
1.0832870
4-5 digit
accura cey
(a) What is the point being made by this table?
11
(b) Based on this table, for large values of n, (1+)" - e'. So a dollar compounded
continuously at 3% will grow to e03 1.030454534 at the end of one year. If you invest
one million dollars compounded continuously at 3%, how much will you have at the end
of one year?
1,030454,534
(c) If you invest $10,000 in an account that pays 8% compounded continuously, how much
will you have at the end of the year?
10,832.87
Generalization: For large values of n, (1+5)" =e"
So if an investment is compounded
continuously, the banking formula is A = P(1+;)" becomes
A=Pert
%3D
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