Simple Interest
Math MCQs

Question :    How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?

Correct Answer  $5500

Solution & Explanation

Solution

Given,

Amount (A) = $6875

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

$6875 = P (1 + 5% × 5)

⇒ $6875 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6875 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6875 = P (1 + ²⁵/₁₀₀)

⇒ $6875 = P (^{100 + 25}/₁₀₀)

⇒ $6875 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6875

⇒ P = ⁶⁸⁷⁵/_¹²⁵/100

⇒ P = 6875 × ¹⁰⁰/₁₂₅

⇒ P = ^{6875 × 100}/₁₂₅

⇒ P = ⁶⁸⁷⁵⁰⁰/₁₂₅

⇒ P = $5500

Thus, the sum borrowed (P) = $5500 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 6875, then the Principal = ¹⁰⁰/₁₂₅ × 6875

= ^{100 × 6875}/₁₂₅

= ⁶⁸⁷⁵⁰⁰/₁₂₅

= 5500

Thus, Principal = $5500

Thus, the sum borrowed = $5500 Answer

Similar Questions

(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?

(2) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?

(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.

(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?

(6) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.

(8) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(9) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

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