Simple Interest
Math MCQs

Question :    David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4800

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $9600

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 = $9600 – $4800 = $4800

Thus, Simple Interest = $4800

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 × 4800}/_{4800 × 10}

= ⁴⁸⁰⁰⁰⁰/₄₈₀₀₀

= 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) = $4800

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $4800 (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 = 10% of Principal

= 10% of $4800

= ¹⁰/₁₀₀ × 4800

= ^{10 × 4800}/₁₀₀

= ⁴⁸⁰⁰⁰/₁₀₀ = 480

Thus, simple Interest for 1 year = $480

Now,

∵ If the simple Interest is $480, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₀ years

∴ If the simple Interest is $4800, then the time = ¹/₄₈₀ × 4800 years

= ^{1 × 4800}/₄₈₀ years

= ⁴⁸⁰⁰/₄₈₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.

(3) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

(4) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(5) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?

(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 4% simple interest?

(7) What amount will be due after 2 years if William borrowed a sum of $3250 at a 6% simple interest?

(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(9) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.

(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.