Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.
Correct Answer
$6386
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5150 ×3/100 × 8
= 5150 × 3 × 8/100
= 15450 × 8/100
= 123600/100
= $1236
Thus, Simple Interest = $1236
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 + $1236
= $6386
Thus, Amount to be paid = $6386 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 3% × 8)
= $5150 + ($5150 ×3/100 × 8)
= $5150 + (5150 × 3 × 8/100)
= $5150 + (15450 × 8/100)
= $5150 + (123600/100)
= $5150 + $1236 = $6386
Thus, Amount (A) to be paid = $6386 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5150, the simple interest in 1 year
= 3/100 × 5150
= 3 × 5150/100
= 15450/100 = $154.5
Thus, simple interest for 1 year = $154.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $154.5 × 8 = $1236
Thus, Simple Interest (SI) = $1236
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1236
= $6386
Thus, Amount to be paid = $6386 Answer
Similar Questions
(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
(2) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(4) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(5) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?
(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.
(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.