Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6600

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

Amount (A) = $11352

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 = $11352 – $6600 = $4752

Thus, Simple Interest = $4752

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 × 4752}/_{6600 × 8}

= ⁴⁷⁵²⁰⁰/₅₂₈₀₀

= 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) = $6600

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

Simple Interest = $4752 (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 $6600

= ⁸/₁₀₀ × 6600

= ^{8 × 6600}/₁₀₀

= ⁵²⁸⁰⁰/₁₀₀ = 528

Thus, simple Interest for 1 year = $528

Now,

∵ If the simple Interest is $528, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₂₈ years

∴ If the simple Interest is $4752, then the time = ¹/₅₂₈ × 4752 years

= ^{1 × 4752}/₅₂₈ years

= ⁴⁷⁵²/₅₂₈ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.

(2) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?

(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.

(5) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(7) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 3% simple interest?

(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.