Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
Correct Answer
$6477
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 9
= $5100 ×3/100 × 9
= 5100 × 3 × 9/100
= 15300 × 9/100
= 137700/100
= $1377
Thus, Simple Interest = $1377
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 + $1377
= $6477
Thus, Amount to be paid = $6477 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) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 3% × 9)
= $5100 + ($5100 ×3/100 × 9)
= $5100 + (5100 × 3 × 9/100)
= $5100 + (15300 × 9/100)
= $5100 + (137700/100)
= $5100 + $1377 = $6477
Thus, Amount (A) to be paid = $6477 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5100, the simple interest in 1 year
= 3/100 × 5100
= 3 × 5100/100
= 15300/100 = $153
Thus, simple interest for 1 year = $153
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $153 × 9 = $1377
Thus, Simple Interest (SI) = $1377
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $1377
= $6477
Thus, Amount to be paid = $6477 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(2) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 4% simple interest?
(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.
(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(6) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?
(8) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.
(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.