Question:
David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7872
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 = $7872 – $4800 = $3072
Thus, Simple Interest = $3072
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 × 3072/4800 × 8
= 307200/38400
= 8 years (using formula)
Thus, Time (T) = 8 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) = $4800
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3072 (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 $4800
= 8/100 × 4800
= 8 × 4800/100
= 38400/100 = 384
Thus, simple Interest for 1 year = $384
Now,
∵ If the simple Interest is $384, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/384 years
∴ If the simple Interest is $3072, then the time = 1/384 × 3072 years
= 1 × 3072/384 years
= 3072/384 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?
(2) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 5% simple interest?
(4) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.
(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?
(6) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?
(8) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?
(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?
(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?