Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6500

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $9230

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9230 – $6500 = $2730

Thus, Simple Interest = $2730

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2730}/_{6500 × 7}

= ²⁷³⁰⁰⁰/₄₅₅₀₀

= 6 years (using formula)

Thus, Time (T) = 6 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $6500

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2730 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 7% of Principal

= 7% of $6500

= ⁷/₁₀₀ × 6500

= ^{7 × 6500}/₁₀₀

= ⁴⁵⁵⁰⁰/₁₀₀ = 455

Thus, simple Interest for 1 year = $455

Now,

∵ If the simple Interest is $455, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₅ years

∴ If the simple Interest is $2730, then the time = ¹/₄₅₅ × 2730 years

= ^{1 × 2730}/₄₅₅ years

= ²⁷³⁰/₄₅₅ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

(2) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.

(3) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(4) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.

(7) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.

(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?

(9) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.

(10) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.