Question:
Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.
Correct Answer
$8480
Solution And Explanation
Solution
Given,
Principal (P) = $5300
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) = $5300 × 6% × 10
= $5300 ×6/100 × 10
= 5300 × 6 × 10/100
= 31800 × 10/100
= 318000/100
= $3180
Thus, Simple Interest = $3180
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 = $5300 + $3180
= $8480
Thus, Amount to be paid = $8480 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 = $5300
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5300 + ($5300 × 6% × 10)
= $5300 + ($5300 ×6/100 × 10)
= $5300 + (5300 × 6 × 10/100)
= $5300 + (31800 × 10/100)
= $5300 + (318000/100)
= $5300 + $3180 = $8480
Thus, Amount (A) to be paid = $8480 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 $5300, the simple interest in 1 year
= 6/100 × 5300
= 6 × 5300/100
= 31800/100 = $318
Thus, simple interest for 1 year = $318
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $318 × 10 = $3180
Thus, Simple Interest (SI) = $3180
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $3180
= $8480
Thus, Amount to be paid = $8480 Answer
Similar Questions
(1) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?
(4) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(5) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(9) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?
(10) Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.