Question:
Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $7238
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $7238 – $4700 = $2538
Thus, Simple Interest = $2538
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 × 2538/4700 × 9
= 253800/42300
= 6 years (using formula)
Thus, Time (T) = 6 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) = $4700
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $2538 (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 = 9% of Principal
= 9% of $4700
= 9/100 × 4700
= 9 × 4700/100
= 42300/100 = 423
Thus, simple Interest for 1 year = $423
Now,
∵ If the simple Interest is $423, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/423 years
∴ If the simple Interest is $2538, then the time = 1/423 × 2538 years
= 1 × 2538/423 years
= 2538/423 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?
(2) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(3) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(4) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.
(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 8% simple interest?
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.
(8) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?