Question:
Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9620
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 = $9620 – $6500 = $3120
Thus, Simple Interest = $3120
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 × 3120/6500 × 6
= 312000/39000
= 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) = $6500
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3120 (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 = 6% of Principal
= 6% of $6500
= 6/100 × 6500
= 6 × 6500/100
= 39000/100 = 390
Thus, simple Interest for 1 year = $390
Now,
∵ If the simple Interest is $390, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/390 years
∴ If the simple Interest is $3120, then the time = 1/390 × 3120 years
= 1 × 3120/390 years
= 3120/390 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
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(2) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(3) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(4) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.
(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?
(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(8) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
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