Question:
Michael took a loan of $4600 at the rate of 9% 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
7
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 9% 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 × 9
= 289800/41400
= 7 years (using formula)
Thus, Time (T) = 7 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) = 9% 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 = 9% of Principal
= 9% of $4600
= 9/100 × 4600
= 9 × 4600/100
= 41400/100 = 414
Thus, simple Interest for 1 year = $414
Now,
∵ If the simple Interest is $414, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/414 years
∴ If the simple Interest is $2898, then the time = 1/414 × 2898 years
= 1 × 2898/414 years
= 2898/414 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.
(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?
(8) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.