Question:
Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10980
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 = $10980 – $6100 = $4880
Thus, Simple Interest = $4880
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 × 4880/6100 × 8
= 488000/48800
= 10 years (using formula)
Thus, Time (T) = 10 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 = $4880 (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 $4880, then the time = 1/488 × 4880 years
= 1 × 4880/488 years
= 4880/488 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.
(3) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(5) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?
(6) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.
(7) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(9) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?