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) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
(4) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?
(5) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.
(7) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.
(8) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?
(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(10) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.