Question:
Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
Correct Answer
$7757.5
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 5%
Time (t) = 9 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% × 9
= $5350 ×5/100 × 9
= 5350 × 5 × 9/100
= 26750 × 9/100
= 240750/100
= $2407.5
Thus, Simple Interest = $2407.5
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 + $2407.5
= $7757.5
Thus, Amount to be paid = $7757.5 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) = 9 years
Thus, Amount (A)
= $5350 + ($5350 × 5% × 9)
= $5350 + ($5350 ×5/100 × 9)
= $5350 + (5350 × 5 × 9/100)
= $5350 + (26750 × 9/100)
= $5350 + (240750/100)
= $5350 + $2407.5 = $7757.5
Thus, Amount (A) to be paid = $7757.5 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 9 years
= Simple interest for 1 year × 9
= $267.5 × 9 = $2407.5
Thus, Simple Interest (SI) = $2407.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $2407.5
= $7757.5
Thus, Amount to be paid = $7757.5 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
(6) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(7) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?
(9) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?
(10) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.