Simple Interest
Math MCQs

Question :    Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6400

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $9472

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 = $9472 – $6400 = $3072

Thus, Simple Interest = $3072

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 × 3072}/_{6400 × 8}

= ³⁰⁷²⁰⁰/₅₁₂₀₀

= 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) = $6400

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3072 (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 = 8% of Principal

= 8% of $6400

= ⁸/₁₀₀ × 6400

= ^{8 × 6400}/₁₀₀

= ⁵¹²⁰⁰/₁₀₀ = 512

Thus, simple Interest for 1 year = $512

Now,

∵ If the simple Interest is $512, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₂ years

∴ If the simple Interest is $3072, then the time = ¹/₅₁₂ × 3072 years

= ^{1 × 3072}/₅₁₂ years

= ³⁰⁷²/₅₁₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?

(2) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.

(3) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(4) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?

(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.

(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?

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

(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?