Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
Correct Answer
$6324
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5100 ×3/100 × 8
= 5100 × 3 × 8/100
= 15300 × 8/100
= 122400/100
= $1224
Thus, Simple Interest = $1224
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 + $1224
= $6324
Thus, Amount to be paid = $6324 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 3% × 8)
= $5100 + ($5100 ×3/100 × 8)
= $5100 + (5100 × 3 × 8/100)
= $5100 + (15300 × 8/100)
= $5100 + (122400/100)
= $5100 + $1224 = $6324
Thus, Amount (A) to be paid = $6324 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5100, the simple interest in 1 year
= 3/100 × 5100
= 3 × 5100/100
= 15300/100 = $153
Thus, simple interest for 1 year = $153
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $153 × 8 = $1224
Thus, Simple Interest (SI) = $1224
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $1224
= $6324
Thus, Amount to be paid = $6324 Answer
Similar Questions
(1) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?
(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(3) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) 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.
(5) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.
(8) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(10) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.