Question:
Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
Correct Answer
$6480
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 2%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5400 × 2% × 10
= $5400 ×2/100 × 10
= 5400 × 2 × 10/100
= 10800 × 10/100
= 108000/100
= $1080
Thus, Simple Interest = $1080
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 = $5400 + $1080
= $6480
Thus, Amount to be paid = $6480 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 = $5400
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5400 + ($5400 × 2% × 10)
= $5400 + ($5400 ×2/100 × 10)
= $5400 + (5400 × 2 × 10/100)
= $5400 + (10800 × 10/100)
= $5400 + (108000/100)
= $5400 + $1080 = $6480
Thus, Amount (A) to be paid = $6480 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5400, the simple interest in 1 year
= 2/100 × 5400
= 2 × 5400/100
= 10800/100 = $108
Thus, simple interest for 1 year = $108
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $108 × 10 = $1080
Thus, Simple Interest (SI) = $1080
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1080
= $6480
Thus, Amount to be paid = $6480 Answer
Similar Questions
(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
(2) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(4) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(7) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(8) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(9) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.