Question:
Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 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) = 7% per annum
Amount (A) = $8965
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 = $8965 – $5500 = $3465
Thus, Simple Interest = $3465
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 × 3465/5500 × 7
= 346500/38500
= 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) = 7% per annum
Simple Interest = $3465 (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 = 7% of Principal
= 7% of $5500
= 7/100 × 5500
= 7 × 5500/100
= 38500/100 = 385
Thus, simple Interest for 1 year = $385
Now,
∵ If the simple Interest is $385, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/385 years
∴ If the simple Interest is $3465, then the time = 1/385 × 3465 years
= 1 × 3465/385 years
= 3465/385 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(2) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(3) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?
(5) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.
(7) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(10) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.