Question:
Matthew took a loan of $6400 at the rate of 8% 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
6
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 8% 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 × 8
= 307200/51200
= 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) = 8% 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 = 8% of Principal
= 8% of $6400
= 8/100 × 6400
= 8 × 6400/100
= 51200/100 = 512
Thus, simple Interest for 1 year = $512
Now,
∵ If the simple Interest is $512, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/512 years
∴ If the simple Interest is $3072, then the time = 1/512 × 3072 years
= 1 × 3072/512 years
= 3072/512 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?
(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(3) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.
(5) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.
(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.
(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?
(9) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.