Question:
Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9620
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 = $9620 – $6500 = $3120
Thus, Simple Interest = $3120
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 × 3120/6500 × 8
= 312000/52000
= 6 years (using formula)
Thus, Time (T) = 6 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 = $3120 (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 $3120, then the time = 1/520 × 3120 years
= 1 × 3120/520 years
= 3120/520 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.
(3) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(4) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 8% simple interest?
(5) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(8) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?
(10) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?