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 Jennifer have to pay after 6 years if he takes a loan of $3250 at 3% simple interest?
(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.
(4) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.
(5) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(9) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?