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) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?
(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(4) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(6) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 9% simple interest?
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
(9) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.