Question:
Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
Correct Answer
$7605
Solution And Explanation
Solution
Given,
Principal (P) = $5850
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) = $5850 × 3% × 10
= $5850 ×3/100 × 10
= 5850 × 3 × 10/100
= 17550 × 10/100
= 175500/100
= $1755
Thus, Simple Interest = $1755
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 = $5850 + $1755
= $7605
Thus, Amount to be paid = $7605 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 = $5850
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5850 + ($5850 × 3% × 10)
= $5850 + ($5850 ×3/100 × 10)
= $5850 + (5850 × 3 × 10/100)
= $5850 + (17550 × 10/100)
= $5850 + (175500/100)
= $5850 + $1755 = $7605
Thus, Amount (A) to be paid = $7605 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 $5850, the simple interest in 1 year
= 3/100 × 5850
= 3 × 5850/100
= 17550/100 = $175.5
Thus, simple interest for 1 year = $175.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $175.5 × 10 = $1755
Thus, Simple Interest (SI) = $1755
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $1755
= $7605
Thus, Amount to be paid = $7605 Answer
Similar Questions
(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?
(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?
(3) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.
(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(6) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(7) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(8) If Steven paid $5152 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 2% simple interest?
(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.