Question:
Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8640
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 = $8640 – $5400 = $3240
Thus, Simple Interest = $3240
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 × 3240/5400 × 6
= 324000/32400
= 10 years (using formula)
Thus, Time (T) = 10 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) = $5400
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3240 (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 $5400
= 6/100 × 5400
= 6 × 5400/100
= 32400/100 = 324
Thus, simple Interest for 1 year = $324
Now,
∵ If the simple Interest is $324, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/324 years
∴ If the simple Interest is $3240, then the time = 1/324 × 3240 years
= 1 × 3240/324 years
= 3240/324 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?
(3) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(4) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?
(7) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?
(8) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(9) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.