Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
Correct Answer
$6936
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 4%
Time (t) = 9 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) = $5100 × 4% × 9
= $5100 ×4/100 × 9
= 5100 × 4 × 9/100
= 20400 × 9/100
= 183600/100
= $1836
Thus, Simple Interest = $1836
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 = $5100 + $1836
= $6936
Thus, Amount to be paid = $6936 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 = $5100
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 4% × 9)
= $5100 + ($5100 ×4/100 × 9)
= $5100 + (5100 × 4 × 9/100)
= $5100 + (20400 × 9/100)
= $5100 + (183600/100)
= $5100 + $1836 = $6936
Thus, Amount (A) to be paid = $6936 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 $5100, the simple interest in 1 year
= 4/100 × 5100
= 4 × 5100/100
= 20400/100 = $204
Thus, simple interest for 1 year = $204
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $204 × 9 = $1836
Thus, Simple Interest (SI) = $1836
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $1836
= $6936
Thus, Amount to be paid = $6936 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?
(5) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?
(7) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?
(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?
(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.