Question:
Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10140
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 = $10140 – $6500 = $3640
Thus, Simple Interest = $3640
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 × 3640/6500 × 8
= 364000/52000
= 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) = $6500
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3640 (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 = 8% of Principal
= 8% of $6500
= 8/100 × 6500
= 8 × 6500/100
= 52000/100 = 520
Thus, simple Interest for 1 year = $520
Now,
∵ If the simple Interest is $520, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/520 years
∴ If the simple Interest is $3640, then the time = 1/520 × 3640 years
= 1 × 3640/520 years
= 3640/520 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.
(2) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(4) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(5) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?
(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(9) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.