Simple Interest
Math MCQs

Question :    Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4500

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

Amount (A) = $8145

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 = $8145 – $4500 = $3645

Thus, Simple Interest = $3645

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 × 3645}/_{4500 × 9}

= ³⁶⁴⁵⁰⁰/₄₀₅₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $4500

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

Simple Interest = $3645 (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 $4500

= ⁹/₁₀₀ × 4500

= ^{9 × 4500}/₁₀₀

= ⁴⁰⁵⁰⁰/₁₀₀ = 405

Thus, simple Interest for 1 year = $405

Now,

∵ If the simple Interest is $405, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₅ years

∴ If the simple Interest is $3645, then the time = ¹/₄₀₅ × 3645 years

= ^{1 × 3645}/₄₀₅ years

= ³⁶⁴⁵/₄₀₅ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?

(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(3) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.

(4) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(5) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(6) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?

(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?

(9) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.