Simple Interest
Math MCQs

Question :    How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?

Correct Answer  $7500

Solution & Explanation

Solution

Given,

Amount (A) = $9375

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

$9375 = P (1 + 5% × 5)

⇒ $9375 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9375 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9375 = P (1 + ²⁵/₁₀₀)

⇒ $9375 = P (^{100 + 25}/₁₀₀)

⇒ $9375 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9375

⇒ P = ⁹³⁷⁵/_¹²⁵/100

⇒ P = 9375 × ¹⁰⁰/₁₂₅

⇒ P = ^{9375 × 100}/₁₂₅

⇒ P = ⁹³⁷⁵⁰⁰/₁₂₅

⇒ P = $7500

Thus, the sum borrowed (P) = $7500 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 9375, then the Principal = ¹⁰⁰/₁₂₅ × 9375

= ^{100 × 9375}/₁₂₅

= ⁹³⁷⁵⁰⁰/₁₂₅

= 7500

Thus, Principal = $7500

Thus, the sum borrowed = $7500 Answer

Similar Questions

(1) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.

(2) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?

(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?

(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.

(6) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(7) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.

(9) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.

(10) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?