Question:
Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9984
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 = $9984 – $6400 = $3584
Thus, Simple Interest = $3584
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 × 3584/6400 × 8
= 358400/51200
= 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) = $6400
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3584 (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 $6400
= 8/100 × 6400
= 8 × 6400/100
= 51200/100 = 512
Thus, simple Interest for 1 year = $512
Now,
∵ If the simple Interest is $512, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/512 years
∴ If the simple Interest is $3584, then the time = 1/512 × 3584 years
= 1 × 3584/512 years
= 3584/512 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?
(2) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(4) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?
(8) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.
(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
(10) 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.