Time to Double or Triple an Investment The formula t = ln m n ln ( 1 + r n ) can be used to find the number of years t required to multiply an investment m times when r is the per annum interest rate compounded n times a year. (a) How many years will it take to double the value of an IRA that compounds annually at the rate of 6 % ? (b) How many years will it take to triple the value of a savings account that compounds quarterly at an annual rate of 5 % ? (c) Give a derivation of this formula.
Time to Double or Triple an Investment The formula t = ln m n ln ( 1 + r n ) can be used to find the number of years t required to multiply an investment m times when r is the per annum interest rate compounded n times a year. (a) How many years will it take to double the value of an IRA that compounds annually at the rate of 6 % ? (b) How many years will it take to triple the value of a savings account that compounds quarterly at an annual rate of 5 % ? (c) Give a derivation of this formula.
Solution Summary: The author explains how the formula can be used to calculate the number of years required to multiply an investment m times the per annum interest rate compounded n times a year.
Time to Double or Triple an Investment
The formula
can be used to find the number of years
required to multiply an investment
times when
is the per annum interest rate compounded
times a year.
(a) How many years will it take to double the value of an IRA that compounds annually at the rate of
?
(b) How many years will it take to triple the value of a savings account that compounds quarterly at an annual rate of
?
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.