Question:
Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $6888
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 = $6888 – $4200 = $2688
Thus, Simple Interest = $2688
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 × 2688/4200 × 8
= 268800/33600
= 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) = $4200
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2688 (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 $4200
= 8/100 × 4200
= 8 × 4200/100
= 33600/100 = 336
Thus, simple Interest for 1 year = $336
Now,
∵ If the simple Interest is $336, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/336 years
∴ If the simple Interest is $2688, then the time = 1/336 × 2688 years
= 1 × 2688/336 years
= 2688/336 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?
(3) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?
(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(7) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.
(9) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(10) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.