Math, asked by rupalidebnath009, 23 hours ago

you borrowed $ 10400 for 4 years at 12.7 and the interest is compounded semi annually.what is the total you will pay back?what is the total you will pay back?​

Answers

Answered by Atlas99
15

Given

  • You borrowed $ 10400 for 4 years at 12.7 and the interest is compounded semi - annually.

To find

  • We have to find total amount that we will pay back.

Solution

In this problem we can see that it is given that interest is compounded semi - annually which means half - yearly.

Whenever interest is compounded half - yearly then we have to multiply the time by 2 and divide the rate by 2.

Like this:-

  • Principal = $10400.
  • Time = 4years= 4×2 = 8years.
  • Rate = 12.7% = 12.7/2 = 6.35%.

We will solve this problem by using simple interest method.

In this method we will find the interest for 8 years separately. Also whatever amount will come for that year will convert into principal for another year.

Let's solve :-

Formula to be used

  • I = P × R × T/100.
  • A = P + I.

For the first year

Principal = $10400.

Rate = 6.35%.

Time = 1year.

I = 10400 × 6.35 × 1/100

=> I = $660.4.

Amount = 10400 + 660.4 = $11060.4

For the second year

Principal = $11060.4.

Rate = 6.35%.

Time = 1year.

I = 11060.4 × 6.35 × 1/100

=> I = $702.34.

Amount = 11060.4 + 702.34 = $11762.74.

For the third year

Principal = $11762.74

Rate = 6.35%

Time = 1year.

I = 11762.74 × 6.35 × 1/100

=> I = $746.93.

Amount = 11762.74 + 746.93

= $12509.67.

For the fourth year

Principal = $12509.67.

Rate = 6.35%.

Time = 1year.

I = 12509.67 × 6.35 × 1/100

=> I = $794.37.

Amount = 12509.67 + 794.37

= $13,304.04.

For the fifth year

Principal = $13,304.04.

Rate = 6.35%.

Time = 1year.

I = 13304.04 × 6.35 × 1/100

=> I = $844.81.

Amount = 13304.04 + 844.81

= 14148.85.

For the sixth year

Principal = $14148.85.

Rate = 6.35%.

Time = 1year.

I = 14148.85 × 6.35 × 1/100

=> I = $898.45.

Amount = 14148.85 + 898.45

= $15047.3.

For the seventh year

Principal = 15047.3.

Rate = 6.35%.

Time = 1year.

I = 15047.3 × 6.35 × 1/100

=> I = $955.50.

Amount = 15047.3 + 955.50

= $16002.8.

For the eighth year

Principal = $16002.8.

Rate = 6.35%.

Time = 1year.

I = 16002.8 × 6.35 × 1/100

=> I = $1016.18.

Final amount = 16002.8 + 1016.18

= $17018.98.

Final Answer

Therefore, $17,018.98 is the total amount I will pay back.

Used Abbreviations

P = Principal.

R = Rate.

T = Time.

I = Simple Interest.

Meaning of some words in Question

Borrowed = Principal.

Total pay back = Amount.

Semi-annually = Half - yearly.

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