Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
Correct Answer
$9690
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 10%
Time (t) = 9 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% × 9
= $5100 ×10/100 × 9
= 5100 × 10 × 9/100
= 51000 × 9/100
= 459000/100
= $4590
Thus, Simple Interest = $4590
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 + $4590
= $9690
Thus, Amount to be paid = $9690 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) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 10% × 9)
= $5100 + ($5100 ×10/100 × 9)
= $5100 + (5100 × 10 × 9/100)
= $5100 + (51000 × 9/100)
= $5100 + (459000/100)
= $5100 + $4590 = $9690
Thus, Amount (A) to be paid = $9690 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 9 years
= Simple interest for 1 year × 9
= $510 × 9 = $4590
Thus, Simple Interest (SI) = $4590
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $4590
= $9690
Thus, Amount to be paid = $9690 Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?
(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?
(3) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(5) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?
(6) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.
(8) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
(10) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.