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) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?
(2) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(3) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(4) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?
(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.
(10) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.