Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
Correct Answer
$8313
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 7%
Time (t) = 9 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% × 9
= $5100 ×7/100 × 9
= 5100 × 7 × 9/100
= 35700 × 9/100
= 321300/100
= $3213
Thus, Simple Interest = $3213
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 + $3213
= $8313
Thus, Amount to be paid = $8313 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) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 7% × 9)
= $5100 + ($5100 ×7/100 × 9)
= $5100 + (5100 × 7 × 9/100)
= $5100 + (35700 × 9/100)
= $5100 + (321300/100)
= $5100 + $3213 = $8313
Thus, Amount (A) to be paid = $8313 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 9 years
= Simple interest for 1 year × 9
= $357 × 9 = $3213
Thus, Simple Interest (SI) = $3213
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3213
= $8313
Thus, Amount to be paid = $8313 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?
(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?
(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?
(4) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(6) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(8) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?
(10) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?