Simple Interest
Math MCQs

Question :    Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6300

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

Amount (A) = $9324

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 = $9324 – $6300 = $3024

Thus, Simple Interest = $3024

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 × 3024}/_{6300 × 8}

= ³⁰²⁴⁰⁰/₅₀₄₀₀

= 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) = $6300

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

Simple Interest = $3024 (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 $6300

= ⁸/₁₀₀ × 6300

= ^{8 × 6300}/₁₀₀

= ⁵⁰⁴⁰⁰/₁₀₀ = 504

Thus, simple Interest for 1 year = $504

Now,

∵ If the simple Interest is $504, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₀₄ years

∴ If the simple Interest is $3024, then the time = ¹/₅₀₄ × 3024 years

= ^{1 × 3024}/₅₀₄ years

= ³⁰²⁴/₅₀₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.

(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.

(4) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.

(5) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?

(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.

(8) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Jennifer had to pay $3640 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.