Question:
Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $6808
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 = $6808 – $4600 = $2208
Thus, Simple Interest = $2208
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 × 2208/4600 × 8
= 220800/36800
= 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) = $4600
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2208 (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 = 8% of Principal
= 8% of $4600
= 8/100 × 4600
= 8 × 4600/100
= 36800/100 = 368
Thus, simple Interest for 1 year = $368
Now,
∵ If the simple Interest is $368, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/368 years
∴ If the simple Interest is $2208, then the time = 1/368 × 2208 years
= 1 × 2208/368 years
= 2208/368 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?
(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 6% simple interest?
(3) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.
(5) If Susan borrowed $3650 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.
(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(9) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.