Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
Correct Answer
$9860
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 10%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 7
= $5800 ×10/100 × 7
= 5800 × 10 × 7/100
= 58000 × 7/100
= 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) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5800 + ($5800 × 10% × 7)
= $5800 + ($5800 ×10/100 × 7)
= $5800 + (5800 × 10 × 7/100)
= $5800 + (58000 × 7/100)
= $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 = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5800, the simple interest in 1 year
= 10/100 × 5800
= 10 × 5800/100
= 58000/100 = $580
Thus, simple interest for 1 year = $580
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $580 × 7 = $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 after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(2) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?
(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?
(5) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(7) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?
(8) How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.
(10) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?