Solved on Nov 22, 2023

Find the monthly payment $PMT$ for a loan with $P=\$25,823$ , $n=80$ , and $i=0.023$ . (Round $PMT$ to two decimal places.)

STEP 1

Assumptions1. The present value (PV) is $25,823. The number of periods (n) is803. The interest rate per period (i) is0.0234. We need to find the payment amount per period (MT)

STEP 2

We can use the formula for the present value of an ordinary annuity to solve for PM. The formula is $PV = PM \times \left(1 - (1 + i)^{-n}\right) / i$

STEP 3

We need to rearrange the formula to solve for PM. We can do this by multiplying both sides of the equation by i and then dividing by the term in the parentheses.
$MT = PV \times i / \left(1 - (1 + i)^{-n}\right)$

STEP 4

Now, plug in the given values for PV, i, and n to calculate PM.
$MT = \$25,823 \times0.023 / \left(1 - (1 +0.023)^{-80}\right)$

STEP 5

Calculate the value of the expression in the parentheses.
$1 - (1 +0.023)^{-80} \approx0.9999$

STEP 6

Substitute this value back into the equation to calculate PM.
$MT = \$25,823 \times0.023 /0.9999$

STEP 7

Calculate the payment amount per period.
$MT = \$25,823 \times0.023 /0.9999 \approx \$595.32$ The payment amount per period is approximately $595.32.

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Find the monthly payment $PMT$ for a loan with $P=\$25,823$ , $n=80$ , and $i=0.023$ . (Round $PMT$ to two decimal places.)

STEP 1

Assumptions1. The present value (PV) is $25,823. The number of periods (n) is803. The interest rate per period (i) is0.0234. We need to find the payment amount per period (MT)

STEP 2

We can use the formula for the present value of an ordinary annuity to solve for PM. The formula is $PV = PM \times \left(1 - (1 + i)^{-n}\right) / i$

STEP 3

We need to rearrange the formula to solve for PM. We can do this by multiplying both sides of the equation by i and then dividing by the term in the parentheses.
$MT = PV \times i / \left(1 - (1 + i)^{-n}\right)$

STEP 4

Now, plug in the given values for PV, i, and n to calculate PM.
$MT = \$25,823 \times0.023 / \left(1 - (1 +0.023)^{-80}\right)$

STEP 5

Calculate the value of the expression in the parentheses.
$1 - (1 +0.023)^{-80} \approx0.9999$

STEP 6

Substitute this value back into the equation to calculate PM.
$MT = \$25,823 \times0.023 /0.9999$

STEP 7

Calculate the payment amount per period.
$MT = \$25,823 \times0.023 /0.9999 \approx \$595.32$ The payment amount per period is approximately $595.32.

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Find the monthly payment PMTPMTPMT for a loan with P=$25,823P=\$25,823P=$25,823, n=80n=80n=80, and i=0.023i=0.023i=0.023. (Round PMTPMTPMT to two decimal places.)

STEP 1

Assumptions1. The present value (PV) is $25,823. The number of periods (n) is803. The interest rate per period (i) is0.0234. We need to find the payment amount per period (MT)

STEP 2

We can use the formula for the present value of an ordinary annuity to solve for PM. The formula isPV=PM×(1−(1+i)−n)/iPV = PM \times \left(1 - (1 + i)^{-n}\right) / iPV=PM×(1−(1+i)−n)/i

STEP 3

We need to rearrange the formula to solve for PM. We can do this by multiplying both sides of the equation by i and then dividing by the term in the parentheses.MT=PV×i/(1−(1+i)−n)MT = PV \times i / \left(1 - (1 + i)^{-n}\right)MT=PV×i/(1−(1+i)−n)

STEP 4

Now, plug in the given values for PV, i, and n to calculate PM.MT=$25,823×0.023/(1−(1+0.023)−80)MT = \$25,823 \times0.023 / \left(1 - (1 +0.023)^{-80}\right)MT=$25,823×0.023/(1−(1+0.023)−80)

STEP 5

Calculate the value of the expression in the parentheses.1−(1+0.023)−80≈0.99991 - (1 +0.023)^{-80} \approx0.99991−(1+0.023)−80≈0.9999

STEP 6

Substitute this value back into the equation to calculate PM.MT=$25,823×0.023/0.9999MT = \$25,823 \times0.023 /0.9999MT=$25,823×0.023/0.9999

STEP 7

Calculate the payment amount per period.MT=$25,823×0.023/0.9999≈$595.32MT = \$25,823 \times0.023 /0.9999 \approx \$595.32MT=$25,823×0.023/0.9999≈$595.32The payment amount per period is approximately $595.32.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the monthly payment $PMT$ for a loan with $P=\$25,823$ , $n=80$ , and $i=0.023$ . (Round $PMT$ to two decimal places.)

We can use the formula for the present value of an ordinary annuity to solve for PM. The formula is $PV = PM \times \left(1 - (1 + i)^{-n}\right) / i$

We need to rearrange the formula to solve for PM. We can do this by multiplying both sides of the equation by i and then dividing by the term in the parentheses.
$MT = PV \times i / \left(1 - (1 + i)^{-n}\right)$

Now, plug in the given values for PV, i, and n to calculate PM.
$MT = \$25,823 \times0.023 / \left(1 - (1 +0.023)^{-80}\right)$

Calculate the value of the expression in the parentheses.
$1 - (1 +0.023)^{-80} \approx0.9999$

Substitute this value back into the equation to calculate PM.
$MT = \$25,823 \times0.023 /0.9999$

Calculate the payment amount per period.
$MT = \$25,823 \times0.023 /0.9999 \approx \$595.32$ The payment amount per period is approximately $595.32.