Question:
Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 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) = 7% per annum
Amount (A) = $7498
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 = $7498 – $4600 = $2898
Thus, Simple Interest = $2898
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 × 2898/4600 × 7
= 289800/32200
= 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) = 7% per annum
Simple Interest = $2898 (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 = 7% of Principal
= 7% of $4600
= 7/100 × 4600
= 7 × 4600/100
= 32200/100 = 322
Thus, simple Interest for 1 year = $322
Now,
∵ If the simple Interest is $322, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/322 years
∴ If the simple Interest is $2898, then the time = 1/322 × 2898 years
= 1 × 2898/322 years
= 2898/322 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(3) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 8% simple interest?
(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(5) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(7) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(10) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.