Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.
Correct Answer
$6728
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 8
= $5800 ×2/100 × 8
= 5800 × 2 × 8/100
= 11600 × 8/100
= 92800/100
= $928
Thus, Simple Interest = $928
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 + $928
= $6728
Thus, Amount to be paid = $6728 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) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5800 + ($5800 × 2% × 8)
= $5800 + ($5800 ×2/100 × 8)
= $5800 + (5800 × 2 × 8/100)
= $5800 + (11600 × 8/100)
= $5800 + (92800/100)
= $5800 + $928 = $6728
Thus, Amount (A) to be paid = $6728 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5800, the simple interest in 1 year
= 2/100 × 5800
= 2 × 5800/100
= 11600/100 = $116
Thus, simple interest for 1 year = $116
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $116 × 8 = $928
Thus, Simple Interest (SI) = $928
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $928
= $6728
Thus, Amount to be paid = $6728 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(2) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(4) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(6) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 4% simple interest?
(9) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.