Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.
Correct Answer
$8268
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5300 ×7/100 × 8
= 5300 × 7 × 8/100
= 37100 × 8/100
= 296800/100
= $2968
Thus, Simple Interest = $2968
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 + $2968
= $8268
Thus, Amount to be paid = $8268 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 7% × 8)
= $5300 + ($5300 ×7/100 × 8)
= $5300 + (5300 × 7 × 8/100)
= $5300 + (37100 × 8/100)
= $5300 + (296800/100)
= $5300 + $2968 = $8268
Thus, Amount (A) to be paid = $8268 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5300, the simple interest in 1 year
= 7/100 × 5300
= 7 × 5300/100
= 37100/100 = $371
Thus, simple interest for 1 year = $371
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $371 × 8 = $2968
Thus, Simple Interest (SI) = $2968
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2968
= $8268
Thus, Amount to be paid = $8268 Answer
Similar Questions
(1) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?
(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(4) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(8) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.
(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?