Question:
Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $12489
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 = $12489 – $6900 = $5589
Thus, Simple Interest = $5589
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 × 5589/6900 × 9
= 558900/62100
= 9 years (using formula)
Thus, Time (T) = 9 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) = 9% per annum
Simple Interest = $5589 (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 $6900
= 9/100 × 6900
= 9 × 6900/100
= 62100/100 = 621
Thus, simple Interest for 1 year = $621
Now,
∵ If the simple Interest is $621, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/621 years
∴ If the simple Interest is $5589, then the time = 1/621 × 5589 years
= 1 × 5589/621 years
= 5589/621 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.
(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?
(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?
(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(9) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?
(10) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.