Question:
John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $6512
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 = $6512 – $4400 = $2112
Thus, Simple Interest = $2112
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 × 2112/4400 × 8
= 211200/35200
= 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) = $4400
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2112 (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 $4400
= 8/100 × 4400
= 8 × 4400/100
= 35200/100 = 352
Thus, simple Interest for 1 year = $352
Now,
∵ If the simple Interest is $352, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/352 years
∴ If the simple Interest is $2112, then the time = 1/352 × 2112 years
= 1 × 2112/352 years
= 2112/352 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(7) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.
(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.