Question:
Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
Correct Answer
$7670
Solution And Explanation
Solution
Given,
Principal (P) = $5900
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) = $5900 × 3% × 10
= $5900 ×3/100 × 10
= 5900 × 3 × 10/100
= 17700 × 10/100
= 177000/100
= $1770
Thus, Simple Interest = $1770
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 + $1770
= $7670
Thus, Amount to be paid = $7670 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) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5900 + ($5900 × 3% × 10)
= $5900 + ($5900 ×3/100 × 10)
= $5900 + (5900 × 3 × 10/100)
= $5900 + (17700 × 10/100)
= $5900 + (177000/100)
= $5900 + $1770 = $7670
Thus, Amount (A) to be paid = $7670 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 $5900, the simple interest in 1 year
= 3/100 × 5900
= 3 × 5900/100
= 17700/100 = $177
Thus, simple interest for 1 year = $177
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $177 × 10 = $1770
Thus, Simple Interest (SI) = $1770
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $1770
= $7670
Thus, Amount to be paid = $7670 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.
(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(3) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.
(6) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 3 years.
(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?
(10) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?