Question:
Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8112
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $8112 – $5200 = $2912
Thus, Simple Interest = $2912
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 2912/5200 × 7
= 291200/36400
= 8 years (using formula)
Thus, Time (T) = 8 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $5200
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2912 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 7% of Principal
= 7% of $5200
= 7/100 × 5200
= 7 × 5200/100
= 36400/100 = 364
Thus, simple Interest for 1 year = $364
Now,
∵ If the simple Interest is $364, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/364 years
∴ If the simple Interest is $2912, then the time = 1/364 × 2912 years
= 1 × 2912/364 years
= 2912/364 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
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(2) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
(4) Anthony had to pay $4687 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.
(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(9) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.
(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.