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) If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?
(3) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.
(5) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(6) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
(7) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.
(10) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.