Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6800

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 = $6800 – $5000 = $1800

Thus, Simple Interest = $1800

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 × 1800}/_{5000 × 6}

= ¹⁸⁰⁰⁰⁰/₃₀₀₀₀

= 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) = $5000

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $1800 (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 = 6% of Principal

= 6% of $5000

= ⁶/₁₀₀ × 5000

= ^{6 × 5000}/₁₀₀

= ³⁰⁰⁰⁰/₁₀₀ = 300

Thus, simple Interest for 1 year = $300

Now,

∵ If the simple Interest is $300, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₀ years

∴ If the simple Interest is $1800, then the time = ¹/₃₀₀ × 1800 years

= ^{1 × 1800}/₃₀₀ years

= ¹⁸⁰⁰/₃₀₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) 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.

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.

(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?

(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.

(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?

(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.

(7) 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.

(8) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.

(10) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.