Question:
Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10318
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 = $10318 – $6700 = $3618
Thus, Simple Interest = $3618
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 × 3618/6700 × 9
= 361800/60300
= 6 years (using formula)
Thus, Time (T) = 6 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) = $6700
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3618 (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 = 9% of Principal
= 9% of $6700
= 9/100 × 6700
= 9 × 6700/100
= 60300/100 = 603
Thus, simple Interest for 1 year = $603
Now,
∵ If the simple Interest is $603, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/603 years
∴ If the simple Interest is $3618, then the time = 1/603 × 3618 years
= 1 × 3618/603 years
= 3618/603 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(2) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?
(4) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(7) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?
(10) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 9% simple interest?