Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.
Correct Answer
$7155
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7
= $5300 ×5/100 × 7
= 5300 × 5 × 7/100
= 26500 × 7/100
= 185500/100
= $1855
Thus, Simple Interest = $1855
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 + $1855
= $7155
Thus, Amount to be paid = $7155 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 5% × 7)
= $5300 + ($5300 ×5/100 × 7)
= $5300 + (5300 × 5 × 7/100)
= $5300 + (26500 × 7/100)
= $5300 + (185500/100)
= $5300 + $1855 = $7155
Thus, Amount (A) to be paid = $7155 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5300, the simple interest in 1 year
= 5/100 × 5300
= 5 × 5300/100
= 26500/100 = $265
Thus, simple interest for 1 year = $265
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $265 × 7 = $1855
Thus, Simple Interest (SI) = $1855
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1855
= $7155
Thus, Amount to be paid = $7155 Answer
Similar Questions
(1) What amount will be due after 2 years if John borrowed a sum of $3100 at a 4% simple interest?
(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 3 years.
(3) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(4) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.
(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.
(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.