Question

Q1: Payments of $ 670 are being made at the end of each month for 5 years at an interest of 8% compounded monthly. Calculate the Present Value.

Answer 1

Answer:

So, the present accumulated value is, $ 49557.69

Step-by-step explanation:

According to the question, payments of $ 670 are being made at the end of each month for 5 years at an interest of 8% compounded monthly. So, present accumulated value, =

$ $\sum_{x = 1}^{60}670 \times (1 + \frac{8}{12 \times 100})^{x}$

= $ $(670 \times (\frac {(1 + \frac {2}{300})^{61} -  ( 1 + \frac{2}{300})}{\frac{2}{300}})$

$\simeq$ $ 49557.69

So, the present accumulated value is, $ 49557.69

Answer 2

Payment of $ 670 with interest every month 8%

Then the payment is made for 5 years

If this year is the fifth year, the total payment is

($ 670 + 8%) x 60 months (1 Year 12 Months, 12 Months multiplied by 5)

($ 670 + $ 53.6 (monthly interest)) x 60

$ 723.6 x 60 = $ 43,416

So, the current value is $ 43,416

Further Explanation

The current value is determined from the following calculation:

8% is the monthly interest on a $ 670 loan

Borrowing is done within a period of 5 years, which is around 60 months (12 months x 5 years)

The formula used is

(Amount of Payment + Monthly Interest) x 5 Years (60 months) = Results

If entered into the value, the calculation is as follows:

Current value = ($ 670 + 8%) x 60

Current value = ($ 670 + 0.8) x 60

Current value = ($ 670 + $ 53.6) x 60

Current value = $ 723.6 x 60

Current value = $ 43,416

The total to be paid for 5 years is $ 43,416

More information

8% interest = 0.8 x 670

So 8% of 670 is 53.6

and monthly payments are the result of the sum of payments and monthly interest, 723.6

Learn More

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Details

Grade: Middle School

Subject: Mathematics/Business

Keyword: loan, interest, payment