Questions: Use the future value formula to find the indicated value. FV = 3816; n = 29; i = 0.06; PMT = ? PMT = (Round to the nearest cent.)

Use the future value formula to find the indicated value. FV = 3816; n = 29; i = 0.06; PMT = ? PMT = (Round to the nearest cent.)
Transcript text: Use the future value formula to find the indicated value. \[ F V=\$ 3816 ; n=29 ; i=0.06 ; \text { PMT }=? \] PMT $=\$$ $\square$ (Round to the nearest cent.)
failed

Solution

failed
failed

Solution Steps

To find the periodic payment (PMT) using the future value of an annuity formula, we can rearrange the formula to solve for PMT. The future value of an annuity formula is given by:

\[ FV = PMT \times \frac{(1 + i)^n - 1}{i} \]

Where:

  • \(FV\) is the future value of the annuity.
  • \(PMT\) is the periodic payment.
  • \(i\) is the interest rate per period.
  • \(n\) is the number of periods.

Rearrange the formula to solve for PMT:

\[ PMT = \frac{FV \times i}{(1 + i)^n - 1} \]

Substitute the given values into the formula to calculate PMT.

Step 1: Identify the Given Values

We are given the following values:

  • Future Value (\(FV\)) = 3816
  • Number of periods (\(n\)) = 29
  • Interest rate per period (\(i\)) = 0.06
Step 2: Use the Future Value of Annuity Formula

The future value of an annuity formula is given by:

\[ FV = PMT \times \frac{(1 + i)^n - 1}{i} \]

To find the periodic payment (\(PMT\)), we rearrange the formula:

\[ PMT = \frac{FV \times i}{(1 + i)^n - 1} \]

Step 3: Substitute the Values and Calculate PMT

Substituting the known values into the rearranged formula:

\[ PMT = \frac{3816 \times 0.06}{(1 + 0.06)^{29} - 1} \]

Calculating the denominator:

\[ (1 + 0.06)^{29} \approx 5.74349 \]

Thus,

\[ PMT = \frac{3816 \times 0.06}{5.74349 - 1} = \frac{229.96}{4.74349} \approx 48.54 \]

After rounding to the nearest cent, we find:

\[ PMT \approx 51.82 \]

Final Answer

The periodic payment (\(PMT\)) is given by:

\[ \boxed{PMT = 51.82} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
10:15 learning.mheducation.com Mc Graw Hill 44 of 59 Concepts completed (i) Multiple Choice Question What is the function of revenue tariffs? To prevent dumping To limit imports of goods and services To raise money for the government To reduce the retail price of imported products so that domestic goods are competitively priced Need help? Review these concept resources. 目 Read About the Concept Rate your confidence to submit your answer.
failedAnswered
Write the slope-intercept form of the equation of the line through the given point with the given slope. 7) through: (1,2), slope = -2 A) y = -5 x + 4 B) y = -2 x + 4 8) through: (1,-2), slope = undefined A) x = -1 B) y = x C) y = -1 D) x = 1
failedAnswered
A 9 - ft ladder leans against the side of a house. How far is the bottom of the ladder from the side of the house when the angle of elevation of the ladder is 62 degrees? Round your answer to the nearest tenth.
failedAnswered
Is it possible to determine the fare for taking the taxi for six miles using linear or exponential growth? If so, what is the fare for taking the taxi for six miles?
failedAnswered
Digger Inc. sells a high-speed retrieval system for mining information. It provides the following information for the year. - Overhead cost: Budgeted 1,378,850, Actual 1,351,850 - Machine hours: Budgeted 56,300, Actual 46,500 - Direct labor hours: Budgeted 109,000, Actual 105,000 Overhead is applied on the basis of direct labor hours. (a) Compute the predetermined overhead rate. (Round answer to 2 decimal places, e.g. 12.25.) Predetermined overhead rate per direct labor hour