Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
Correct Answer
$6695
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 3%
Time (t) = 10 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% × 10
= $5150 ×3/100 × 10
= 5150 × 3 × 10/100
= 15450 × 10/100
= 154500/100
= $1545
Thus, Simple Interest = $1545
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 + $1545
= $6695
Thus, Amount to be paid = $6695 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) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 3% × 10)
= $5150 + ($5150 ×3/100 × 10)
= $5150 + (5150 × 3 × 10/100)
= $5150 + (15450 × 10/100)
= $5150 + (154500/100)
= $5150 + $1545 = $6695
Thus, Amount (A) to be paid = $6695 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 10 years
= Simple interest for 1 year × 10
= $154.5 × 10 = $1545
Thus, Simple Interest (SI) = $1545
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1545
= $6695
Thus, Amount to be paid = $6695 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?
(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(4) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 4% simple interest?
(6) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.
(9) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
(10) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.