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) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(3) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.
(4) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(6) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.
(9) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.