Question:
Lisa took a loan of $6100 at the rate of 7% 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
8
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 7% 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 × 7
= 341600/42700
= 8 years (using formula)
Thus, Time (T) = 8 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) = 7% 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 = 7% of Principal
= 7% of $6100
= 7/100 × 6100
= 7 × 6100/100
= 42700/100 = 427
Thus, simple Interest for 1 year = $427
Now,
∵ If the simple Interest is $427, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/427 years
∴ If the simple Interest is $3416, then the time = 1/427 × 3416 years
= 1 × 3416/427 years
= 3416/427 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?
(2) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(6) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.
(8) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.