Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.
Correct Answer
$7599
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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) = $5100 × 7% × 7
= $5100 ×7/100 × 7
= 5100 × 7 × 7/100
= 35700 × 7/100
= 249900/100
= $2499
Thus, Simple Interest = $2499
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 + $2499
= $7599
Thus, Amount to be paid = $7599 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) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5100 + ($5100 × 7% × 7)
= $5100 + ($5100 ×7/100 × 7)
= $5100 + (5100 × 7 × 7/100)
= $5100 + (35700 × 7/100)
= $5100 + (249900/100)
= $5100 + $2499 = $7599
Thus, Amount (A) to be paid = $7599 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 $5100, the simple interest in 1 year
= 7/100 × 5100
= 7 × 5100/100
= 35700/100 = $357
Thus, simple interest for 1 year = $357
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $357 × 7 = $2499
Thus, Simple Interest (SI) = $2499
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $2499
= $7599
Thus, Amount to be paid = $7599 Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?
(3) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(4) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?
(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.
(9) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.
(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?