Question:
Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
Correct Answer
$7490
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 4%
Time (t) = 10 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) = $5350 × 4% × 10
= $5350 ×4/100 × 10
= 5350 × 4 × 10/100
= 21400 × 10/100
= 214000/100
= $2140
Thus, Simple Interest = $2140
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 = $5350 + $2140
= $7490
Thus, Amount to be paid = $7490 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 = $5350
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5350 + ($5350 × 4% × 10)
= $5350 + ($5350 ×4/100 × 10)
= $5350 + (5350 × 4 × 10/100)
= $5350 + (21400 × 10/100)
= $5350 + (214000/100)
= $5350 + $2140 = $7490
Thus, Amount (A) to be paid = $7490 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 $5350, the simple interest in 1 year
= 4/100 × 5350
= 4 × 5350/100
= 21400/100 = $214
Thus, simple interest for 1 year = $214
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $214 × 10 = $2140
Thus, Simple Interest (SI) = $2140
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $2140
= $7490
Thus, Amount to be paid = $7490 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(2) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.
(4) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(6) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.
(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(8) 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.
(9) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.