Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5100

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

Amount (A) = $9180

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 = $9180 – $5100 = $4080

Thus, Simple Interest = $4080

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 × 4080}/_{5100 × 10}

= ⁴⁰⁸⁰⁰⁰/₅₁₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $5100

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

Simple Interest = $4080 (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 $5100

= ¹⁰/₁₀₀ × 5100

= ^{10 × 5100}/₁₀₀

= ⁵¹⁰⁰⁰/₁₀₀ = 510

Thus, simple Interest for 1 year = $510

Now,

∵ If the simple Interest is $510, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₀ years

∴ If the simple Interest is $4080, then the time = ¹/₅₁₀ × 4080 years

= ^{1 × 4080}/₅₁₀ years

= ⁴⁰⁸⁰/₅₁₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?

(2) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?

(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 2% simple interest?

(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?

(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 4% simple interest?

(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?

(8) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.

(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.

(10) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.