Simple Interest
Math MCQs

Question :    How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?

Correct Answer  $7450

Solution & Explanation

Solution

Given,

Amount (A) = $9312.5

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

$9312.5 = P (1 + 5% × 5)

⇒ $9312.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9312.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9312.5 = P (1 + ²⁵/₁₀₀)

⇒ $9312.5 = P (^{100 + 25}/₁₀₀)

⇒ $9312.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9312.5

⇒ P = ^9312.5/_¹²⁵/100

⇒ P = 9312.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9312.5 × 100}/₁₂₅

⇒ P = ⁹³¹²⁵⁰/₁₂₅

⇒ P = $7450

Thus, the sum borrowed (P) = $7450 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 9312.5, then the Principal = ¹⁰⁰/₁₂₅ × 9312.5

= ^{100 × 9312.5}/₁₂₅

= ⁹³¹²⁵⁰/₁₂₅

= 7450

Thus, Principal = $7450

Thus, the sum borrowed = $7450 Answer

Similar Questions

(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?

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

(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?

(4) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.

(5) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.

(7) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?

(8) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

(9) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 2% simple interest?