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) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(3) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?
(5) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.
(6) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(9) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.