Simple Interest
Math MCQs

Question :    How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?

Correct Answer  $5600

Solution & Explanation

Solution

Given,

Amount (A) = $7000

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

$7000 = P (1 + 5% × 5)

⇒ $7000 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7000 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7000 = P (1 + ²⁵/₁₀₀)

⇒ $7000 = P (^{100 + 25}/₁₀₀)

⇒ $7000 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7000

⇒ P = ⁷⁰⁰⁰/_¹²⁵/100

⇒ P = 7000 × ¹⁰⁰/₁₂₅

⇒ P = ^{7000 × 100}/₁₂₅

⇒ P = ⁷⁰⁰⁰⁰⁰/₁₂₅

⇒ P = $5600

Thus, the sum borrowed (P) = $5600 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 7000, then the Principal = ¹⁰⁰/₁₂₅ × 7000

= ^{100 × 7000}/₁₂₅

= ⁷⁰⁰⁰⁰⁰/₁₂₅

= 5600

Thus, Principal = $5600

Thus, the sum borrowed = $5600 Answer

Similar Questions

(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?

(2) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.

(3) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?

(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.

(5) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.

(6) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 4% simple interest?

(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.

(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.