Question:
Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
Correct Answer
$7888
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 4%
Time (t) = 9 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) = $5800 × 4% × 9
= $5800 ×4/100 × 9
= 5800 × 4 × 9/100
= 23200 × 9/100
= 208800/100
= $2088
Thus, Simple Interest = $2088
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 = $5800 + $2088
= $7888
Thus, Amount to be paid = $7888 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 = $5800
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5800 + ($5800 × 4% × 9)
= $5800 + ($5800 ×4/100 × 9)
= $5800 + (5800 × 4 × 9/100)
= $5800 + (23200 × 9/100)
= $5800 + (208800/100)
= $5800 + $2088 = $7888
Thus, Amount (A) to be paid = $7888 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 $5800, the simple interest in 1 year
= 4/100 × 5800
= 4 × 5800/100
= 23200/100 = $232
Thus, simple interest for 1 year = $232
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $232 × 9 = $2088
Thus, Simple Interest (SI) = $2088
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $2088
= $7888
Thus, Amount to be paid = $7888 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(2) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) If Andrew paid $5760 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
(5) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(6) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?
(8) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(9) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(10) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.