Question:
Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10212
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 = $10212 – $6900 = $3312
Thus, Simple Interest = $3312
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 × 3312/6900 × 8
= 331200/55200
= 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) = $6900
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3312 (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 = 8% of Principal
= 8% of $6900
= 8/100 × 6900
= 8 × 6900/100
= 55200/100 = 552
Thus, simple Interest for 1 year = $552
Now,
∵ If the simple Interest is $552, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/552 years
∴ If the simple Interest is $3312, then the time = 1/552 × 3312 years
= 1 × 3312/552 years
= 3312/552 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(2) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(4) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(6) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?
(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?
(8) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.
(9) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.