Question:
Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9088
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 = $9088 – $6400 = $2688
Thus, Simple Interest = $2688
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 × 2688/6400 × 6
= 268800/38400
= 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) = $6400
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2688 (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 $6400
= 6/100 × 6400
= 6 × 6400/100
= 38400/100 = 384
Thus, simple Interest for 1 year = $384
Now,
∵ If the simple Interest is $384, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/384 years
∴ If the simple Interest is $2688, then the time = 1/384 × 2688 years
= 1 × 2688/384 years
= 2688/384 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 7% simple interest?
(2) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.
(3) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 8 years.
(6) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(7) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
(8) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?
(9) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.