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) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
(2) Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(4) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 4 years.
(6) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(8) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(10) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?