Question:
Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
Correct Answer
$9860
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 10
= $5800 ×7/100 × 10
= 5800 × 7 × 10/100
= 40600 × 10/100
= 406000/100
= $4060
Thus, Simple Interest = $4060
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 + $4060
= $9860
Thus, Amount to be paid = $9860 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5800 + ($5800 × 7% × 10)
= $5800 + ($5800 ×7/100 × 10)
= $5800 + (5800 × 7 × 10/100)
= $5800 + (40600 × 10/100)
= $5800 + (406000/100)
= $5800 + $4060 = $9860
Thus, Amount (A) to be paid = $9860 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5800, the simple interest in 1 year
= 7/100 × 5800
= 7 × 5800/100
= 40600/100 = $406
Thus, simple interest for 1 year = $406
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $406 × 10 = $4060
Thus, Simple Interest (SI) = $4060
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $4060
= $9860
Thus, Amount to be paid = $9860 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(2) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(3) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.
(5) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?
(7) Anthony had to pay $4687 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.