Question:
Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
Correct Answer
$10200
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 10%
Time (t) = 10 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) = $5100 × 10% × 10
= $5100 ×10/100 × 10
= 5100 × 10 × 10/100
= 51000 × 10/100
= 510000/100
= $5100
Thus, Simple Interest = $5100
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 = $5100 + $5100
= $10200
Thus, Amount to be paid = $10200 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 = $5100
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5100 + ($5100 × 10% × 10)
= $5100 + ($5100 ×10/100 × 10)
= $5100 + (5100 × 10 × 10/100)
= $5100 + (51000 × 10/100)
= $5100 + (510000/100)
= $5100 + $5100 = $10200
Thus, Amount (A) to be paid = $10200 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 $5100, the simple interest in 1 year
= 10/100 × 5100
= 10 × 5100/100
= 51000/100 = $510
Thus, simple interest for 1 year = $510
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $510 × 10 = $5100
Thus, Simple Interest (SI) = $5100
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $5100
= $10200
Thus, Amount to be paid = $10200 Answer
Similar Questions
(1) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(3) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.
(6) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(7) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.
(10) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.