Simple Interest
Math MCQs

Question :    How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?

Correct Answer  $5800

Solution & Explanation

Solution

Given,

Amount (A) = $7250

Rate of Simple Interest (R) = 5%

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

$7250 = P (1 + 5% × 5)

⇒ $7250 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7250 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7250 = P (1 + ²⁵/₁₀₀)

⇒ $7250 = P (^{100 + 25}/₁₀₀)

⇒ $7250 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7250

⇒ P = ⁷²⁵⁰/_¹²⁵/100

⇒ P = 7250 × ¹⁰⁰/₁₂₅

⇒ P = ^{7250 × 100}/₁₂₅

⇒ P = ⁷²⁵⁰⁰⁰/₁₂₅

⇒ P = $5800

Thus, the sum borrowed (P) = $5800 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 7250, then the Principal = ¹⁰⁰/₁₂₅ × 7250

= ^{100 × 7250}/₁₂₅

= ⁷²⁵⁰⁰⁰/₁₂₅

= 5800

Thus, Principal = $5800

Thus, the sum borrowed = $5800 Answer

Similar Questions

(1) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?

(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 6% simple interest?

(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.

(4) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?

(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.

(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.

(8) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?

(9) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.