Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $8624

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 = $8624 – $5600 = $3024

Thus, Simple Interest = $3024

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 × 3024}/_{5600 × 9}

= ³⁰²⁴⁰⁰/₅₀₄₀₀

= 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) = $5600

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

Simple Interest = $3024 (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 $5600

= ⁹/₁₀₀ × 5600

= ^{9 × 5600}/₁₀₀

= ⁵⁰⁴⁰⁰/₁₀₀ = 504

Thus, simple Interest for 1 year = $504

Now,

∵ If the simple Interest is $504, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₀₄ years

∴ If the simple Interest is $3024, then the time = ¹/₅₀₄ × 3024 years

= ^{1 × 3024}/₅₀₄ years

= ³⁰²⁴/₅₀₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?

(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?

(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(4) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.

(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?

(6) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.

(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?

(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.

(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.