Question:
Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
Correct Answer
$8400
Solution And Explanation
Solution
Given,
Principal (P) = $5250
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5250 × 6% × 10
= $5250 ×6/100 × 10
= 5250 × 6 × 10/100
= 31500 × 10/100
= 315000/100
= $3150
Thus, Simple Interest = $3150
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 = $5250 + $3150
= $8400
Thus, Amount to be paid = $8400 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 = $5250
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5250 + ($5250 × 6% × 10)
= $5250 + ($5250 ×6/100 × 10)
= $5250 + (5250 × 6 × 10/100)
= $5250 + (31500 × 10/100)
= $5250 + (315000/100)
= $5250 + $3150 = $8400
Thus, Amount (A) to be paid = $8400 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5250, the simple interest in 1 year
= 6/100 × 5250
= 6 × 5250/100
= 31500/100 = $315
Thus, simple interest for 1 year = $315
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $315 × 10 = $3150
Thus, Simple Interest (SI) = $3150
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $3150
= $8400
Thus, Amount to be paid = $8400 Answer
Similar Questions
(1) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.
(3) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?
(6) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(7) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.
(10) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.