Question:
Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7498
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 = $7498 – $4600 = $2898
Thus, Simple Interest = $2898
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 × 2898/4600 × 7
= 289800/32200
= 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) = $4600
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2898 (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 $4600
= 7/100 × 4600
= 7 × 4600/100
= 32200/100 = 322
Thus, simple Interest for 1 year = $322
Now,
∵ If the simple Interest is $322, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/322 years
∴ If the simple Interest is $2898, then the time = 1/322 × 2898 years
= 1 × 2898/322 years
= 2898/322 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?
(4) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.
(7) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.