Question:
Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9632
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 = $9632 – $5600 = $4032
Thus, Simple Interest = $4032
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 × 4032/5600 × 9
= 403200/50400
= 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) = $5600
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4032 (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 $5600
= 9/100 × 5600
= 9 × 5600/100
= 50400/100 = 504
Thus, simple Interest for 1 year = $504
Now,
∵ If the simple Interest is $504, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/504 years
∴ If the simple Interest is $4032, then the time = 1/504 × 4032 years
= 1 × 4032/504 years
= 4032/504 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(2) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.
(4) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 6% simple interest?
(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(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) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?
(10) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.