Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $12420

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 = $12420 – $6900 = $5520

Thus, Simple Interest = $5520

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 × 5520}/_{6900 × 8}

= ⁵⁵²⁰⁰⁰/₅₅₂₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = 8% per annum

Simple Interest = $5520 (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 $6900

= ⁸/₁₀₀ × 6900

= ^{8 × 6900}/₁₀₀

= ⁵⁵²⁰⁰/₁₀₀ = 552

Thus, simple Interest for 1 year = $552

Now,

∵ If the simple Interest is $552, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₅₂ years

∴ If the simple Interest is $5520, then the time = ¹/₅₅₂ × 5520 years

= ^{1 × 5520}/₅₅₂ years

= ⁵⁵²⁰/₅₅₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?

(2) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?

(3) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.

(5) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.

(7) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.

(8) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.

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

(10) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?