Question:
Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9676
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 = $9676 – $5900 = $3776
Thus, Simple Interest = $3776
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 × 3776/5900 × 8
= 377600/47200
= 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) = $5900
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3776 (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 = 8% of Principal
= 8% of $5900
= 8/100 × 5900
= 8 × 5900/100
= 47200/100 = 472
Thus, simple Interest for 1 year = $472
Now,
∵ If the simple Interest is $472, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/472 years
∴ If the simple Interest is $3776, then the time = 1/472 × 3776 years
= 1 × 3776/472 years
= 3776/472 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
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(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.
(3) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.
(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?
(5) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?
(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.
(9) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?
(10) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.