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

Question

nirvana33 [79]

3 years ago

14

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.

Mathematics

2 answers:

zhuklara [117] · Answer 1 · 2022-06-13T02:30:42+03:00

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 $1 + r + r^{2} + r^{3} + .......... + r^{n} = 1 \times \frac{r^{n + 1} -1}{r - 1}$ }

Ugo [173] · Answer 2 · 2022-06-13T04:30:18+03:00

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

<h2>Further Explanation</h2><h3>2 Ways to Calculate Loan Interest </h3>

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)