Simple Interest
Math MCQs

Question :    How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?

Correct Answer  $6700

Solution & Explanation

Solution

Given,

Amount (A) = $7705

Rate of Simple Interest (R) = 3%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$7705 = P (1 + 3% × 5)

⇒ $7705 = P (1 + ³/₁₀₀ × 5)

⇒ $7705 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7705 = P (1 + ¹⁵/₁₀₀)

⇒ $7705 = P (^{100 + 15}/₁₀₀)

⇒ $7705 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7705

⇒ P = ⁷⁷⁰⁵/_¹¹⁵/100

⇒ P = 7705 × ¹⁰⁰/₁₁₅

⇒ P = ^{7705 × 100}/₁₁₅

⇒ P = ⁷⁷⁰⁵⁰⁰/₁₁₅

⇒ P = $6700

Thus, the sum borrowed (P) = $6700 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 7705, then the Principal = ¹⁰⁰/₁₁₅ × 7705

= ^{100 × 7705}/₁₁₅

= ⁷⁷⁰⁵⁰⁰/₁₁₅

= 6700

Thus, Principal = $6700

Thus, the sum borrowed = $6700 Answer

Similar Questions

(1) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.

(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.

(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(4) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.

(7) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?

(9) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.

(10) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?