Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.
Correct Answer
$6798
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5150 × 4% × 8
= $5150 ×4/100 × 8
= 5150 × 4 × 8/100
= 20600 × 8/100
= 164800/100
= $1648
Thus, Simple Interest = $1648
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 = $5150 + $1648
= $6798
Thus, Amount to be paid = $6798 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 = $5150
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 4% × 8)
= $5150 + ($5150 ×4/100 × 8)
= $5150 + (5150 × 4 × 8/100)
= $5150 + (20600 × 8/100)
= $5150 + (164800/100)
= $5150 + $1648 = $6798
Thus, Amount (A) to be paid = $6798 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5150, the simple interest in 1 year
= 4/100 × 5150
= 4 × 5150/100
= 20600/100 = $206
Thus, simple interest for 1 year = $206
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $206 × 8 = $1648
Thus, Simple Interest (SI) = $1648
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1648
= $6798
Thus, Amount to be paid = $6798 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(2) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?
(3) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(4) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 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 8% simple interest for 3 years.
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?
(7) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(9) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.