Question:
Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
Correct Answer
$6955
Solution And Explanation
Solution
Given,
Principal (P) = $5350
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) = $5350 × 3% × 10
= $5350 ×3/100 × 10
= 5350 × 3 × 10/100
= 16050 × 10/100
= 160500/100
= $1605
Thus, Simple Interest = $1605
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 = $5350 + $1605
= $6955
Thus, Amount to be paid = $6955 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 = $5350
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5350 + ($5350 × 3% × 10)
= $5350 + ($5350 ×3/100 × 10)
= $5350 + (5350 × 3 × 10/100)
= $5350 + (16050 × 10/100)
= $5350 + (160500/100)
= $5350 + $1605 = $6955
Thus, Amount (A) to be paid = $6955 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 $5350, the simple interest in 1 year
= 3/100 × 5350
= 3 × 5350/100
= 16050/100 = $160.5
Thus, simple interest for 1 year = $160.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $160.5 × 10 = $1605
Thus, Simple Interest (SI) = $1605
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $1605
= $6955
Thus, Amount to be paid = $6955 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.
(2) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(3) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(6) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.
(7) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(9) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?