Question:
Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $6396
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 = $6396 – $4100 = $2296
Thus, Simple Interest = $2296
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 × 2296/4100 × 7
= 229600/28700
= 8 years (using formula)
Thus, Time (T) = 8 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) = $4100
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2296 (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 $4100
= 7/100 × 4100
= 7 × 4100/100
= 28700/100 = 287
Thus, simple Interest for 1 year = $287
Now,
∵ If the simple Interest is $287, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/287 years
∴ If the simple Interest is $2296, then the time = 1/287 × 2296 years
= 1 × 2296/287 years
= 2296/287 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
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(2) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.
(4) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(5) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.
(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?
(8) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(9) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.
(10) 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.