Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.
Correct Answer
$7844
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 6%
Time (t) = 8 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% × 8
= $5300 ×6/100 × 8
= 5300 × 6 × 8/100
= 31800 × 8/100
= 254400/100
= $2544
Thus, Simple Interest = $2544
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 + $2544
= $7844
Thus, Amount to be paid = $7844 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) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 6% × 8)
= $5300 + ($5300 ×6/100 × 8)
= $5300 + (5300 × 6 × 8/100)
= $5300 + (31800 × 8/100)
= $5300 + (254400/100)
= $5300 + $2544 = $7844
Thus, Amount (A) to be paid = $7844 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 8 years
= Simple interest for 1 year × 8
= $318 × 8 = $2544
Thus, Simple Interest (SI) = $2544
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2544
= $7844
Thus, Amount to be paid = $7844 Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?
(2) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(3) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(4) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?
(5) If Richard borrowed $3600 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?
(7) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.
(8) Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(10) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.