Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
Correct Answer
$9120
Solution And Explanation
Solution
Given,
Principal (P) = $5700
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) = $5700 × 6% × 10
= $5700 ×6/100 × 10
= 5700 × 6 × 10/100
= 34200 × 10/100
= 342000/100
= $3420
Thus, Simple Interest = $3420
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 + $3420
= $9120
Thus, Amount to be paid = $9120 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) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 6% × 10)
= $5700 + ($5700 ×6/100 × 10)
= $5700 + (5700 × 6 × 10/100)
= $5700 + (34200 × 10/100)
= $5700 + (342000/100)
= $5700 + $3420 = $9120
Thus, Amount (A) to be paid = $9120 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 10 years
= Simple interest for 1 year × 10
= $342 × 10 = $3420
Thus, Simple Interest (SI) = $3420
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3420
= $9120
Thus, Amount to be paid = $9120 Answer
Similar Questions
(1) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 4 years.
(2) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.
(5) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.
(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?
(7) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.