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) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 4 years.
(4) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?
(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(7) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(10) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?