Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
Correct Answer
$6732
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5100 × 4% × 8
= $5100 ×4/100 × 8
= 5100 × 4 × 8/100
= 20400 × 8/100
= 163200/100
= $1632
Thus, Simple Interest = $1632
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 = $5100 + $1632
= $6732
Thus, Amount to be paid = $6732 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 = $5100
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 4% × 8)
= $5100 + ($5100 ×4/100 × 8)
= $5100 + (5100 × 4 × 8/100)
= $5100 + (20400 × 8/100)
= $5100 + (163200/100)
= $5100 + $1632 = $6732
Thus, Amount (A) to be paid = $6732 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5100, the simple interest in 1 year
= 4/100 × 5100
= 4 × 5100/100
= 20400/100 = $204
Thus, simple interest for 1 year = $204
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $204 × 8 = $1632
Thus, Simple Interest (SI) = $1632
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $1632
= $6732
Thus, Amount to be paid = $6732 Answer
Similar Questions
(1) 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?
(2) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 6% simple interest?
(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.
(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(6) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(8) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
(10) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.