Simple Interest
Math MCQs

Question :    Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5400

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

Amount (A) = $8640

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 = $8640 – $5400 = $3240

Thus, Simple Interest = $3240

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 × 3240}/_{5400 × 10}

= ³²⁴⁰⁰⁰/₅₄₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5400

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

Simple Interest = $3240 (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 $5400

= ¹⁰/₁₀₀ × 5400

= ^{10 × 5400}/₁₀₀

= ⁵⁴⁰⁰⁰/₁₀₀ = 540

Thus, simple Interest for 1 year = $540

Now,

∵ If the simple Interest is $540, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₀ years

∴ If the simple Interest is $3240, then the time = ¹/₅₄₀ × 3240 years

= ^{1 × 3240}/₅₄₀ years

= ³²⁴⁰/₅₄₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?

(2) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.

(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?

(5) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?

(7) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.

(8) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?

(9) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.