Question:
Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7084
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 = $7084 – $4600 = $2484
Thus, Simple Interest = $2484
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 × 2484/4600 × 6
= 248400/27600
= 9 years (using formula)
Thus, Time (T) = 9 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) = $4600
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2484 (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 $4600
= 6/100 × 4600
= 6 × 4600/100
= 27600/100 = 276
Thus, simple Interest for 1 year = $276
Now,
∵ If the simple Interest is $276, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/276 years
∴ If the simple Interest is $2484, then the time = 1/276 × 2484 years
= 1 × 2484/276 years
= 2484/276 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) 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?
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(3) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(4) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
(6) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(7) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(8) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?
(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?
(10) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?