Question:
Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
Correct Answer
$7800
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 5%
Time (t) = 10 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) = $5200 × 5% × 10
= $5200 ×5/100 × 10
= 5200 × 5 × 10/100
= 26000 × 10/100
= 260000/100
= $2600
Thus, Simple Interest = $2600
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 = $5200 + $2600
= $7800
Thus, Amount to be paid = $7800 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 = $5200
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5200 + ($5200 × 5% × 10)
= $5200 + ($5200 ×5/100 × 10)
= $5200 + (5200 × 5 × 10/100)
= $5200 + (26000 × 10/100)
= $5200 + (260000/100)
= $5200 + $2600 = $7800
Thus, Amount (A) to be paid = $7800 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 $5200, the simple interest in 1 year
= 5/100 × 5200
= 5 × 5200/100
= 26000/100 = $260
Thus, simple interest for 1 year = $260
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $260 × 10 = $2600
Thus, Simple Interest (SI) = $2600
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2600
= $7800
Thus, Amount to be paid = $7800 Answer
Similar Questions
(1) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(2) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?
(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?
(5) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 4% simple interest?
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.
(10) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?