Question:
Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $8580
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 = $8580 – $5500 = $3080
Thus, Simple Interest = $3080
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 × 3080/5500 × 8
= 308000/44000
= 7 years (using formula)
Thus, Time (T) = 7 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) = $5500
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3080 (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 $5500
= 8/100 × 5500
= 8 × 5500/100
= 44000/100 = 440
Thus, simple Interest for 1 year = $440
Now,
∵ If the simple Interest is $440, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/440 years
∴ If the simple Interest is $3080, then the time = 1/440 × 3080 years
= 1 × 3080/440 years
= 3080/440 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(2) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
(3) If Karen borrowed $3950 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
(5) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(6) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?
(7) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?
(9) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.
(10) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.