Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?
Correct Answer
$4185
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 7%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 5
= $3100 ×7/100 × 5
= 3100 × 7 × 5/100
= 21700 × 5/100
= 108500/100
= $1085
Thus, Simple Interest = $1085
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 + $1085
= $4185
Thus, Amount to be paid = $4185 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) = 7%
And, Time (t) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 7% × 5)
= $3100 + ($3100 ×7/100 × 5)
= $3100 + (3100 × 7 × 5/100)
= $3100 + (21700 × 5/100)
= $3100 + (108500/100)
= $3100 + $1085 = $4185
Thus, Amount (A) to be paid = $4185 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3100, the simple interest in 1 year
= 7/100 × 3100
= 7 × 3100/100
= 21700/100 = $217
Thus, simple interest for 1 year = $217
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $217 × 5 = $1085
Thus, Simple Interest (SI) = $1085
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1085
= $4185
Thus, Amount to be paid = $4185 Answer
Similar Questions
(1) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.
(4) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.
(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(6) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?
(7) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
(8) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(10) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?