Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.
Correct Answer
$8584
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5800 × 6% × 8
= $5800 ×6/100 × 8
= 5800 × 6 × 8/100
= 34800 × 8/100
= 278400/100
= $2784
Thus, Simple Interest = $2784
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 = $5800 + $2784
= $8584
Thus, Amount to be paid = $8584 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 = $5800
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5800 + ($5800 × 6% × 8)
= $5800 + ($5800 ×6/100 × 8)
= $5800 + (5800 × 6 × 8/100)
= $5800 + (34800 × 8/100)
= $5800 + (278400/100)
= $5800 + $2784 = $8584
Thus, Amount (A) to be paid = $8584 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5800, the simple interest in 1 year
= 6/100 × 5800
= 6 × 5800/100
= 34800/100 = $348
Thus, simple interest for 1 year = $348
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $348 × 8 = $2784
Thus, Simple Interest (SI) = $2784
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $2784
= $8584
Thus, Amount to be paid = $8584 Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.
(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(3) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(4) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?
(6) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(7) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?
(9) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.