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) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?
(2) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
(3) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?
(5) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?
(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
(9) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.
(10) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.