Simple Interest
Math MCQs

Question :    Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.

Correct Answer  $7965

Solution & Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (SI) = 5%

Time (t) = 7 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) = $5900 × 5% × 7

= $5900 ×⁵/₁₀₀ × 7

= ^{5900 × 5 × 7}/₁₀₀

= ^{29500 × 7}/₁₀₀

= ²⁰⁶⁵⁰⁰/₁₀₀

= $2065

Thus, Simple Interest = $2065

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 = $5900 + $2065

= $7965

Thus, Amount to be paid = $7965 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 = $5900

Rate of Simple Interest (SI) or (R) = 5%

And, Time (t) = 7 years

Thus, Amount (A)

= $5900 + ($5900 × 5% × 7)

= $5900 + ($5900 ×⁵/₁₀₀ × 7)

= $5900 + (^{5900 × 5 × 7}/₁₀₀)

= $5900 + (^{29500 × 7}/₁₀₀)

= $5900 + (²⁰⁶⁵⁰⁰/₁₀₀)

= $5900 + $2065 = $7965

Thus, Amount (A) to be paid = $7965 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 $5900, the simple interest in 1 year

= ⁵/₁₀₀ × 5900

= ^{5 × 5900}/₁₀₀

= ²⁹⁵⁰⁰/₁₀₀ = $295

Thus, simple interest for 1 year = $295

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $295 × 7 = $2065

Thus, Simple Interest (SI) = $2065

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5900 + $2065

= $7965

Thus, Amount to be paid = $7965 Answer

Similar Questions

(1) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?

(2) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?

(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.

(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?

(5) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?

(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?

(8) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.

(9) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.