A person purchases a certain product by paying 8 successive monthly installments of $3,400.00 each, paying the first 5 months after the purchase. What is the cash price of the product, if an interest rate of 4% is being charged bi-monthly, capitalized each month? How much is paid each month?

Name: Solved: A person purchases a certain product by paying 8 successive monthly installments of $3,400.00 each, paying the first 5 months after the purchase. What is the cash price of the product, if an interest rate of 4% is being charged bi-monthly, capitalized each month? How much is paid each month? - MathMaster
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Answer to a math question A person purchases a certain product by paying 8 successive monthly installments of $3,400.00 each, paying the first 5 months after the purchase. What is the cash price of the product, if an interest rate of 4% is being charged bi-monthly, capitalized each month? How much is paid each month?

$Expert avatar$

Adonis

4.4

104 Answers

P = 3400

r = \frac{0.04}{12}

n = 8

Step 1: Calculate the present value (cash price) using the annuity due formula:

PV = 3400 \times \frac{1 - (1 + \frac{0.04}{12})^{-8}}{\frac{0.04}{12}}

Step 2: Calculate $ (1 + \frac{0.04}{12})^{-8} $:

(1 + \frac{0.04}{12})^{-8} \approx 0.969198

Step 3: Plug in the value:

PV = 3400 \times \frac{1 - 0.969198}{0.003333}

PV = 3400 \times \frac{0.030802}{0.003333}

PV \approx 3400 \times 9.240

PV \approx 31,464

Step 4: Monthly payment is given as:

\text{Monthly Payment} = 3400

Final Result:

PV \approx 31,464.00

\text{Monthly Payment} = 3400.00

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