Question:
Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 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) = 6% per annum
Amount (A) = $8732
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 = $8732 – $5900 = $2832
Thus, Simple Interest = $2832
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 × 2832/5900 × 6
= 283200/35400
= 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) = 6% per annum
Simple Interest = $2832 (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 $5900
= 6/100 × 5900
= 6 × 5900/100
= 35400/100 = 354
Thus, simple Interest for 1 year = $354
Now,
∵ If the simple Interest is $354, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/354 years
∴ If the simple Interest is $2832, then the time = 1/354 × 2832 years
= 1 × 2832/354 years
= 2832/354 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(2) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 8 years.
(4) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?
(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?
(6) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.
(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?
(10) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.