Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6900

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $11247

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 = $11247 – $6900 = $4347

Thus, Simple Interest = $4347

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 × 4347}/_{6900 × 9}

= ⁴³⁴⁷⁰⁰/₆₂₁₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $6900

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4347 (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 = 9% of Principal

= 9% of $6900

= ⁹/₁₀₀ × 6900

= ^{9 × 6900}/₁₀₀

= ⁶²¹⁰⁰/₁₀₀ = 621

Thus, simple Interest for 1 year = $621

Now,

∵ If the simple Interest is $621, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₂₁ years

∴ If the simple Interest is $4347, then the time = ¹/₆₂₁ × 4347 years

= ^{1 × 4347}/₆₂₁ years

= ⁴³⁴⁷/₆₂₁ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?

(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?

(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

(4) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?

(8) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.

(10) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?