Question:
Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 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) = 6% per annum
Amount (A) = $8662
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 = $8662 – $6100 = $2562
Thus, Simple Interest = $2562
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 × 2562/6100 × 6
= 256200/36600
= 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) = 6% per annum
Simple Interest = $2562 (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 = 6% of Principal
= 6% of $6100
= 6/100 × 6100
= 6 × 6100/100
= 36600/100 = 366
Thus, simple Interest for 1 year = $366
Now,
∵ If the simple Interest is $366, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/366 years
∴ If the simple Interest is $2562, then the time = 1/366 × 2562 years
= 1 × 2562/366 years
= 2562/366 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.
(3) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?
(5) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(6) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?
(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(9) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.