Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.
Correct Answer
$7788
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5900 × 4% × 8
= $5900 ×4/100 × 8
= 5900 × 4 × 8/100
= 23600 × 8/100
= 188800/100
= $1888
Thus, Simple Interest = $1888
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 = $5900 + $1888
= $7788
Thus, Amount to be paid = $7788 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 = $5900
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 4% × 8)
= $5900 + ($5900 ×4/100 × 8)
= $5900 + (5900 × 4 × 8/100)
= $5900 + (23600 × 8/100)
= $5900 + (188800/100)
= $5900 + $1888 = $7788
Thus, Amount (A) to be paid = $7788 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5900, the simple interest in 1 year
= 4/100 × 5900
= 4 × 5900/100
= 23600/100 = $236
Thus, simple interest for 1 year = $236
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $236 × 8 = $1888
Thus, Simple Interest (SI) = $1888
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $1888
= $7788
Thus, Amount to be paid = $7788 Answer
Similar Questions
(1) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?
(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(4) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(5) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 3% simple interest?
(7) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(8) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(10) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.