Question:
Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11880
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 = $11880 – $6600 = $5280
Thus, Simple Interest = $5280
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 × 5280/6600 × 10
= 528000/66000
= 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) = $6600
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5280 (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 $6600
= 10/100 × 6600
= 10 × 6600/100
= 66000/100 = 660
Thus, simple Interest for 1 year = $660
Now,
∵ If the simple Interest is $660, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/660 years
∴ If the simple Interest is $5280, then the time = 1/660 × 5280 years
= 1 × 5280/660 years
= 5280/660 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.
(3) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(5) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.
(7) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?
(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(9) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.