Click here to access the Explore It in a new window. Fuppose you invest $1 in an account that is compounded continuously and you wish to double your money. (a) How many years will it take for the money to double when the interest rate is 1%? (Enter your answer to the nearest hundredth of a year.) 69.31 v yrs (b) How many years will it take for the money to double when the interest rate is 2%? (Enter your answer to the nearest hundredth of a year.) 34.66 v yrs (c) How many years will it take for the money to double when the interest rate is 4%? (Enter your answer to the nearest hundredth of a year.) 17.33 v yrs (d) How many years will it take for the money to double again (that is, for the initial investment of $1 to be worth $4) when the interest rate is 4%? (Enter your answer to the nearest hundredth of a year.) x yrs (e) How many years will it take for the money to double yet again (that is, for the initial investment of $1 to be worth $8) when the interest rate is 4%? (Enter your answer to the nearest hundredth of a year.) X yrs (O For the case of continuous compounding, what do the results of parts (a) through (c) above suggest about the effect doubling the interest rate will have on the length of time it takes for an initial investment to double in value? O The length of time will be halved. O The length of time will be doubled. O The length of time will be quadrupled. (9) For the case of continuous compounding and a fixed interest rate, what do the results of parts (c) through (e) above suggest about the length of time it takes for an initial amount of money to double? The length of time is always the same. The length of time increases as the value of the money increases.
Click here to access the Explore It in a new window. Fuppose you invest $1 in an account that is compounded continuously and you wish to double your money. (a) How many years will it take for the money to double when the interest rate is 1%? (Enter your answer to the nearest hundredth of a year.) 69.31 v yrs (b) How many years will it take for the money to double when the interest rate is 2%? (Enter your answer to the nearest hundredth of a year.) 34.66 v yrs (c) How many years will it take for the money to double when the interest rate is 4%? (Enter your answer to the nearest hundredth of a year.) 17.33 v yrs (d) How many years will it take for the money to double again (that is, for the initial investment of $1 to be worth $4) when the interest rate is 4%? (Enter your answer to the nearest hundredth of a year.) x yrs (e) How many years will it take for the money to double yet again (that is, for the initial investment of $1 to be worth $8) when the interest rate is 4%? (Enter your answer to the nearest hundredth of a year.) X yrs (O For the case of continuous compounding, what do the results of parts (a) through (c) above suggest about the effect doubling the interest rate will have on the length of time it takes for an initial investment to double in value? O The length of time will be halved. O The length of time will be doubled. O The length of time will be quadrupled. (9) For the case of continuous compounding and a fixed interest rate, what do the results of parts (c) through (e) above suggest about the length of time it takes for an initial amount of money to double? The length of time is always the same. The length of time increases as the value of the money increases.
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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I need help with parts d and e!
Transcribed Image Text:Click here to access the Explore It in a new window.
Suppose you invest $1 in an account that is compounded continuously and you wish to double your money.
(a) How many years will it take for the money to double when the interest rate is 1%? (Enter your answer to the nearest hundredth of a year.)
69.31
v yrs
(b) How many years will it take for the money to double when the interest rate is 2%? (Enter your answer to the nearest hundredth of a year.)
34.66
v yrs
(c) How many years will it take for the money to double when the interest rate is 4%? (Enter your answer to the nearest hundredth of a year.)
17.33
v yrs
(d) How many years will it take for the money to double again (that is, for the initial investment of $1 to be worth $4) when the interest rate is 4%? (Enter your answer to the nearest hundredth of
a year.)
X yrs
(e) How many years will it take for the money to double yet again (that is, for the initial investment of $1 to be worth $8) when the interest rate is 4%? (Enter your answer to the nearest hundredth
of a year.)
X yrs
(f) For the case of continuous compounding, what do the results of parts (a) through (c) above suggest about the effect doubling the interest rate will have on the length of time it takes for an initial
investment to double in value?
O The length of time will be halved.
O The length of time will be doubled.
O The length of time will be quadrupled.
(g) For the case of continuous compounding and a fixed interest rate, what do the results of parts (c) through (e) above suggest about the length of time it takes for an initial amount of money to
double?
O The length of time Is always the same.
The length of time increases as the value of the money increases.
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