Question:
Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10664
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 = $10664 – $6200 = $4464
Thus, Simple Interest = $4464
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 × 4464/6200 × 9
= 446400/55800
= 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) = $6200
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4464 (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 $6200
= 9/100 × 6200
= 9 × 6200/100
= 55800/100 = 558
Thus, simple Interest for 1 year = $558
Now,
∵ If the simple Interest is $558, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/558 years
∴ If the simple Interest is $4464, then the time = 1/558 × 4464 years
= 1 × 4464/558 years
= 4464/558 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?
(5) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.
(8) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(9) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.
(10) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.