Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $8930

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 = $8930 – $4700 = $4230

Thus, Simple Interest = $4230

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 × 4230}/_{4700 × 10}

= ⁴²³⁰⁰⁰/₄₇₀₀₀

= 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) = $4700

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

Simple Interest = $4230 (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 $4700

= ¹⁰/₁₀₀ × 4700

= ^{10 × 4700}/₁₀₀

= ⁴⁷⁰⁰⁰/₁₀₀ = 470

Thus, simple Interest for 1 year = $470

Now,

∵ If the simple Interest is $470, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₀ years

∴ If the simple Interest is $4230, then the time = ¹/₄₇₀ × 4230 years

= ^{1 × 4230}/₄₇₀ years

= ⁴²³⁰/₄₇₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(2) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.

(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.

(5) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.

(6) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?

(9) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?

(10) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.