Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
Correct Answer
$4650
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 10%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $3100 × 10% × 5
= $3100 ×10/100 × 5
= 3100 × 10 × 5/100
= 31000 × 5/100
= 155000/100
= $1550
Thus, Simple Interest = $1550
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1550
= $4650
Thus, Amount to be paid = $4650 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $3100
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 10% × 5)
= $3100 + ($3100 ×10/100 × 5)
= $3100 + (3100 × 10 × 5/100)
= $3100 + (31000 × 5/100)
= $3100 + (155000/100)
= $3100 + $1550 = $4650
Thus, Amount (A) to be paid = $4650 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3100, the simple interest in 1 year
= 10/100 × 3100
= 10 × 3100/100
= 31000/100 = $310
Thus, simple interest for 1 year = $310
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $310 × 5 = $1550
Thus, Simple Interest (SI) = $1550
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1550
= $4650
Thus, Amount to be paid = $4650 Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(2) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(4) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(6) How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?
(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(9) If Karen borrowed $3950 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?