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
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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