Question:
Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
Correct Answer
$8778
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 6%
Time (t) = 9 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) = $5700 × 6% × 9
= $5700 ×6/100 × 9
= 5700 × 6 × 9/100
= 34200 × 9/100
= 307800/100
= $3078
Thus, Simple Interest = $3078
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 = $5700 + $3078
= $8778
Thus, Amount to be paid = $8778 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 = $5700
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5700 + ($5700 × 6% × 9)
= $5700 + ($5700 ×6/100 × 9)
= $5700 + (5700 × 6 × 9/100)
= $5700 + (34200 × 9/100)
= $5700 + (307800/100)
= $5700 + $3078 = $8778
Thus, Amount (A) to be paid = $8778 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 $5700, the simple interest in 1 year
= 6/100 × 5700
= 6 × 5700/100
= 34200/100 = $342
Thus, simple interest for 1 year = $342
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $342 × 9 = $3078
Thus, Simple Interest (SI) = $3078
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3078
= $8778
Thus, Amount to be paid = $8778 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?
(2) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
(5) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
(6) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?
(7) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.
(9) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.