Question:
Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
Correct Answer
$9280
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 6%
Time (t) = 10 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% × 10
= $5800 ×6/100 × 10
= 5800 × 6 × 10/100
= 34800 × 10/100
= 348000/100
= $3480
Thus, Simple Interest = $3480
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 + $3480
= $9280
Thus, Amount to be paid = $9280 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) = 10 years
Thus, Amount (A)
= $5800 + ($5800 × 6% × 10)
= $5800 + ($5800 ×6/100 × 10)
= $5800 + (5800 × 6 × 10/100)
= $5800 + (34800 × 10/100)
= $5800 + (348000/100)
= $5800 + $3480 = $9280
Thus, Amount (A) to be paid = $9280 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 10 years
= Simple interest for 1 year × 10
= $348 × 10 = $3480
Thus, Simple Interest (SI) = $3480
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $3480
= $9280
Thus, Amount to be paid = $9280 Answer
Similar Questions
(1) What amount will be due after 2 years if John borrowed a sum of $3100 at a 6% simple interest?
(2) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(3) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 10% simple interest?
(6) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(7) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.
(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?