Question:
Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8704
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 = $8704 – $6400 = $2304
Thus, Simple Interest = $2304
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 × 2304/6400 × 6
= 230400/38400
= 6 years (using formula)
Thus, Time (T) = 6 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 = $2304 (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 $2304, then the time = 1/384 × 2304 years
= 1 × 2304/384 years
= 2304/384 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
(2) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(6) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.
(9) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?