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) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(2) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(3) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(4) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?
(6) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 3 years.
(8) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.