Question:
John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 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) = 7% per annum
Amount (A) = $6248
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 = $6248 – $4400 = $1848
Thus, Simple Interest = $1848
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 × 1848/4400 × 7
= 184800/30800
= 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) = 7% per annum
Simple Interest = $1848 (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 = 7% of Principal
= 7% of $4400
= 7/100 × 4400
= 7 × 4400/100
= 30800/100 = 308
Thus, simple Interest for 1 year = $308
Now,
∵ If the simple Interest is $308, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/308 years
∴ If the simple Interest is $1848, then the time = 1/308 × 1848 years
= 1 × 1848/308 years
= 1848/308 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(2) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(4) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 4 years.
(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?
(9) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?