Question:
Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7810
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 = $7810 – $5500 = $2310
Thus, Simple Interest = $2310
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 × 2310/5500 × 7
= 231000/38500
= 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) = $5500
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2310 (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 $2310, then the time = 1/385 × 2310 years
= 1 × 2310/385 years
= 2310/385 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
(2) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(3) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(5) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.
(7) Jennifer had to pay $3640 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
(10) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?