Question:
Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $12350
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 = $12350 – $6500 = $5850
Thus, Simple Interest = $5850
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 × 5850/6500 × 9
= 585000/58500
= 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) = $6500
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $5850 (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 $6500
= 9/100 × 6500
= 9 × 6500/100
= 58500/100 = 585
Thus, simple Interest for 1 year = $585
Now,
∵ If the simple Interest is $585, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/585 years
∴ If the simple Interest is $5850, then the time = 1/585 × 5850 years
= 1 × 5850/585 years
= 5850/585 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?
(3) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(4) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(5) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.
(7) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 3 years.
(9) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.