Question:
Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.
Correct Answer
$7490
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5350 ×5/100 × 8
= 5350 × 5 × 8/100
= 26750 × 8/100
= 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5350 + ($5350 × 5% × 8)
= $5350 + ($5350 ×5/100 × 8)
= $5350 + (5350 × 5 × 8/100)
= $5350 + (26750 × 8/100)
= $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 = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5350, the simple interest in 1 year
= 5/100 × 5350
= 5 × 5350/100
= 26750/100 = $267.5
Thus, simple interest for 1 year = $267.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $267.5 × 8 = $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) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(2) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(3) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(4) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(5) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(8) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(9) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.
(10) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?