Use properties of rational exponents to solve the compound interest formula for the interest rate, r. For the following exercises, use the compound interest formula, A(t) = P(1 + r/n)nt.

For the following exercises, use the compound interest formula, A(t) = P(1 + r/n)^nt.

Use properties of rational exponents to solve the compound interest formula for the interest rate, r.

Expert Solution

Consider the Compound Interest formula;

A(t) = P(1 + r/n)nt

Where, A(t) is the account value, “t” is the measured in years, “P” is the starting amount or initial value, “r” is the annual percentage rate (APR), “n” is the number of compounding periods in one year.

Use the compound interest formula to find the interest rate r;

A(t)/P = (1 + r/n)nt

Therefore,

{A(t)/P}1/nt = (1 + r/n)

Therefore,

{A(t)/P}1/nt – 1 = r/n

Therefore,

n × [{A(t)/P}1/nt – 1] = r

Therefore,

r = n × [{A(t)/P}1/nt – 1]

Therefore, the compound interest formula for the interest rate, r is r = n × [{A(t)/P}1/nt – 1].

Junaid answered 1 year ago

use the continuous compound interest formula to find the indicated value. A= $76,000 P=$57,756 R=6.1% T=...

use the continuous compound interest formula to find the indicated value. A= $76,000 P=$57,756 R=6.1% T= ? Don’t round until the final answer. Then round to two decimal places as needed.

Solve the following problems by using the binomial formula. a. If n = 4 and p...

Solve the following problems by using the binomial formula. a. If n = 4 and p = 0.45, find P(x = 3). b. If n = 7 and p = 0.75, find P(x = 4). c. If n = 10 and p = 0.75, find P(x ≥ 7). d. If n = 12 and p = 0.60, find P(5 ≤ x ≤ 7).

1) The Compound Interest Formula Suppose ? dollars are invested at a stated annual interest rate...

1) The Compound Interest Formula Suppose ? dollars are invested at a stated annual interest rate r. If interest is compounded n times per year, then the future value of the investment after t years is given by ?(?) = ? ( 1 + ?? )?? . a) Suppose you invest $20,000 at a stated annual interest rate of 6% and that interest is compounded monthly. How much will your investment be worth in 5 years? Round to the nearest...

Let 0 < r < 1 be an interest rate. Consider the following compound investment schemes:...

Let 0 < r < 1 be an interest rate. Consider the following compound investment schemes: Scheme I: Interest is compounded at a rate of r at the end of every month. Scheme II: Interest is compounded at a rate of 3r at the end of every third month. Scheme III: Interest is compounded at a rate of 6r at the end of every sixth month. Question 1 Suppose that you invest R dollars on January 1st. Rank these three...

- Solve the following recurrence relation : T(n) = T(αn) + T((1 − α)n) + n

6. Solve the following recurrence relations t(n) = t(n-1) + 3 for n>1 t(1) = 0...

6. Solve the following recurrence relations t(n) = t(n-1) + 3 for n>1 t(1) = 0 t(n) = t(n-1) + n for n>1 t(1) = 1 t(n) = 3t(n/2) + n for n>1, n is a power of 2 t(1) = ½ t(n) = 6t(n-1) – 9t(n-2) for n>1 t(0) = 0 t(1) = 1

An initial investment amount P, an annual interest rate r, and a time t are given....

An initial investment amount P, an annual interest rate r, and a time t are given. Find the future value of the investment when the interest is compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. Then find (e) the doubling time T for the given interest rate. Round to the nearest cent or nearest tenth of a year as needed. P= $750, r=2.03%, t=11 yr

Use recursion tree to solve the recurrence: T(n) = T(n/15) + T(n/10) + 2T(n/6) + n^(1/2)

The formula for the amount A in an investment account with a nominal interest rate r at any time t is given by A(t) = a(e)rt, where a is the

The formula for the amount A in an investment account with a nominal interest rate r at any time t is given by A(t) = a(e)rt, where a is the amount of principal initially deposited into an account that compounds continuously. Prove that the percentage of interest earned to principal at any time t can be calculated with the formula I(t) = ert − 1.

1. Assume the following recursive formula: R(n)=R(n-1)nn where R(0)=1 The code might look like this: public double...

1. Assume the following recursive formula: R(n)=R(n-1)*n*n where R(0)=1 The code might look like this: public double R(n) { If n==0 return 1 else return R(n-1); } a. What is the recurrence relation showing the number of multiplications for the recursive function R(n) and program? b. Solve the recurrence relation. 2. Show the following is true for all integers n > 1 using mathematical induction: 3. Sort the following list into alphabetical order using selection sort. Write the list showing the swapped...

Question

Use properties of rational exponents to solve the compound interest formula for the interest rate, r. For the following exercises, use the compound interest formula, A(t) = P(1 + r/n)nt.

Solutions

Expert Solution

Related Solutions

use the continuous compound interest formula to find the indicated value. A= $76,000 P=$57,756 R=6.1% T=...

Solve the following problems by using the binomial formula. a. If n = 4 and p...

1) The Compound Interest Formula Suppose ? dollars are invested at a stated annual interest rate...

Let 0 < r < 1 be an interest rate. Consider the following compound investment schemes:...

- Solve the following recurrence relation : T(n) = T(αn) + T((1 − α)n) + n

6. Solve the following recurrence relations t(n) = t(n-1) + 3 for n>1 t(1) = 0...

An initial investment amount P, an annual interest rate r, and a time t are given....

Use recursion tree to solve the recurrence: T(n) = T(n/15) + T(n/10) + 2T(n/6) + n^(1/2)

The formula for the amount A in an investment account with a nominal interest rate r at any time t is given by A(t) = a(e)rt, where a is the

1. Assume the following recursive formula: R(n)=R(n-1)nn where R(0)=1 The code might look like this: public double...