Question:
Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9516
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 = $9516 – $6100 = $3416
Thus, Simple Interest = $3416
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 × 3416/6100 × 8
= 341600/48800
= 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) = $6100
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3416 (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 $6100
= 8/100 × 6100
= 8 × 6100/100
= 48800/100 = 488
Thus, simple Interest for 1 year = $488
Now,
∵ If the simple Interest is $488, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/488 years
∴ If the simple Interest is $3416, then the time = 1/488 × 3416 years
= 1 × 3416/488 years
= 3416/488 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(5) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?
(6) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?
(7) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?
(8) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.