Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.

Correct Answer  $8778

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (SI) = 6%

Time (t) = 9 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5700 × 6% × 9

= $5700 ×⁶/₁₀₀ × 9

= ^{5700 × 6 × 9}/₁₀₀

= ^{34200 × 9}/₁₀₀

= ³⁰⁷⁸⁰⁰/₁₀₀

= $3078

Thus, Simple Interest = $3078

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 = $5700 + $3078

= $8778

Thus, Amount to be paid = $8778 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 = $5700

Rate of Simple Interest (SI) or (R) = 6%

And, Time (t) = 9 years

Thus, Amount (A)

= $5700 + ($5700 × 6% × 9)

= $5700 + ($5700 ×⁶/₁₀₀ × 9)

= $5700 + (^{5700 × 6 × 9}/₁₀₀)

= $5700 + (^{34200 × 9}/₁₀₀)

= $5700 + (³⁰⁷⁸⁰⁰/₁₀₀)

= $5700 + $3078 = $8778

Thus, Amount (A) to be paid = $8778 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 6%

This, means, $6 per $100 per year

∵ For $100, the simple interest for 1 year = $6

∴ For $1, the simple interest for 1 year = ⁶/₁₀₀

∴ For $5700, the simple interest in 1 year

= ⁶/₁₀₀ × 5700

= ^{6 × 5700}/₁₀₀

= ³⁴²⁰⁰/₁₀₀ = $342

Thus, simple interest for 1 year = $342

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $342 × 9 = $3078

Thus, Simple Interest (SI) = $3078

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5700 + $3078

= $8778

Thus, Amount to be paid = $8778 Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

(2) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?

(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 6% simple interest?

(5) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.

(7) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(8) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.