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:

$50,281.04

Step-by-step explanation:

5 years is equivalent to (5 × 12) = 60 months

Now, the first payment $670 is compounded for 60 months at the rate of $\frac{8}{12} = 0.667$% monthly interest.

So, it will become $670(1 + \frac{0.667}{100})^{60} = 670(1.0067)^{60}$.

Similarly the second payment of $670 will become $670(1.0067)^{59}$

Therefore, in this way after 60 months i.e. 5 years the total sum will be

= $670 + 670(1.0067)^{1} + 670(1.0067)^{2} + 670(1.0067)^{3} + ........ + 670(1.0067)^{59} + 670(1.0067)^{60}$

= $670[1 + (1.0067) + (1.0067)^{2} + (1.0067)^{3} + ....... + (1.0067)^{59} + (1.0067)^{60} ]$

= $670[1 \times \frac{(1.0067)^{61} - 1 }{1.0067 - 1} ]$

= $50,281.04 (Answer)

{Since, the sum of the G.P. series $1 + r + r^{2} + r^{3} + .......... + r^{n} = 1 \times \frac{r^{n + 1} -1}{r - 1}$ }

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

2 Ways to Calculate Loan Interest

Flat flowers

To make it easier for you to illustrate this flat interest calculation, the following is an example of the case: Mr. A applied for an unsecured loan of 240 million dollars with a repayment period of 12 months and a loan interest of 10% annually. This is an installment that must be paid by Mr. A every month.

Amount of loan: 240 million

Interest per year: 10%

Duration: 12 months

Principal installments:

$ 240 million: 12 months = $ 20 million / month

Flower:

($ 240 million X 10%): 12 months = $ 2 million

Installments every month:

$ 20 million + $ 2 million = $ 22 million

Effective interest

Thus is the illustration: Mr. B applied for a loan of $ 240 million. How many installments must be paid each month:

To calculate the interest the formula is: PL x i x (30/360)

PL: principal loan balance from the previous month

i: annual interest rates

30: number of days in a month

360: number of days in a year

Principal loan: $ 240 million

Interest: 10% per year

Credit period: 24 months

Month 1 installments:

= $ 240 million X 10% X (30 days / 360 days)

= $ 2 million

Principal installments plus interest in month 1 = $ 10 million + $ 2 million = $ 12 million.

Month installments 2:

= $ 230 million X 10% X (30 days / 360 days)

= $ 1,191,666.67

Learn More

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Details

Grade: Middle School

Subject: Mathematics/Business

Keyword: loan, interest, payment