Question:
( 1 of 10 ) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(A) 4 47/50 Or, 247/50
(B) 8 47/50 Or, 447/50
(C) 4 141/50 Or, 341/50
(D) 4 94/50 Or, 294/50
You selected
13.5
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7052
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 = $7052 – $4100 = $2952
Thus, Simple Interest = $2952
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 × 2952/4100 × 8
= 295200/32800
= 9 years (using formula)
Thus, Time (T) = 9 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) = $4100
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2952 (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 $4100
= 8/100 × 4100
= 8 × 4100/100
= 32800/100 = 328
Thus, simple Interest for 1 year = $328
Now,
∵ If the simple Interest is $328, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/328 years
∴ If the simple Interest is $2952, then the time = 1/328 × 2952 years
= 1 × 2952/328 years
= 2952/328 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 3 years.
(2) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 5% simple interest?
(5) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.
(7) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.