Question:
James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6160
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 = $6160 – $4000 = $2160
Thus, Simple Interest = $2160
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 × 2160/4000 × 6
= 216000/24000
= 9 years (using formula)
Thus, Time (T) = 9 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) = $4000
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2160 (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 $4000
= 6/100 × 4000
= 6 × 4000/100
= 24000/100 = 240
Thus, simple Interest for 1 year = $240
Now,
∵ If the simple Interest is $240, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/240 years
∴ If the simple Interest is $2160, then the time = 1/240 × 2160 years
= 1 × 2160/240 years
= 2160/240 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
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(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?
(4) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(5) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(9) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
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