Question:
Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7384
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 = $7384 – $5200 = $2184
Thus, Simple Interest = $2184
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 × 2184/5200 × 6
= 218400/31200
= 7 years (using formula)
Thus, Time (T) = 7 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) = $5200
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2184 (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 = 6% of Principal
= 6% of $5200
= 6/100 × 5200
= 6 × 5200/100
= 31200/100 = 312
Thus, simple Interest for 1 year = $312
Now,
∵ If the simple Interest is $312, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/312 years
∴ If the simple Interest is $2184, then the time = 1/312 × 2184 years
= 1 × 2184/312 years
= 2184/312 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?
(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(3) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(5) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 4 years.
(7) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(8) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
(9) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?
(10) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.