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
(1) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(4) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(5) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(7) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(8) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?