Question:
Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10450
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 = $10450 – $5500 = $4950
Thus, Simple Interest = $4950
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 × 4950/5500 × 10
= 495000/55000
= 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) = $5500
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4950 (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 = 10% of Principal
= 10% of $5500
= 10/100 × 5500
= 10 × 5500/100
= 55000/100 = 550
Thus, simple Interest for 1 year = $550
Now,
∵ If the simple Interest is $550, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/550 years
∴ If the simple Interest is $4950, then the time = 1/550 × 4950 years
= 1 × 4950/550 years
= 4950/550 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.
(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?
(5) If David paid $4080 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 Susan borrowed a sum of $3650 at 6% simple interest for 4 years.
(7) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(8) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(10) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.