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 $10764 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $10764

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 = $10764 – $6900 = $3864

Thus, Simple Interest = $3864

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 × 3864}/_{6900 × 8}

= ³⁸⁶⁴⁰⁰/₅₅₂₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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 = $3864 (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 $3864, then the time = ¹/₅₅₂ × 3864 years

= ^{1 × 3864}/₅₅₂ years

= ³⁸⁶⁴/₅₅₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 9% simple interest?

(2) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.

(4) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.

(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?

(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.

(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(10) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.