Question:
Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10710
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 = $10710 – $6300 = $4410
Thus, Simple Interest = $4410
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 × 4410/6300 × 10
= 441000/63000
= 7 years (using formula)
Thus, Time (T) = 7 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) = $6300
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4410 (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 = 10% of Principal
= 10% of $6300
= 10/100 × 6300
= 10 × 6300/100
= 63000/100 = 630
Thus, simple Interest for 1 year = $630
Now,
∵ If the simple Interest is $630, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/630 years
∴ If the simple Interest is $4410, then the time = 1/630 × 4410 years
= 1 × 4410/630 years
= 4410/630 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 9% simple interest?
(2) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(6) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.
(10) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?