Question:
Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9472
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 = $9472 – $6400 = $3072
Thus, Simple Interest = $3072
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 × 3072/6400 × 6
= 307200/38400
= 8 years (using formula)
Thus, Time (T) = 8 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 = $3072 (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 $3072, then the time = 1/384 × 3072 years
= 1 × 3072/384 years
= 3072/384 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?
(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?
(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?
(6) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(7) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(8) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
(9) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.