Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $12420

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 = $12420 – $6900 = $5520

Thus, Simple Interest = $5520

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 × 5520}/_{6900 × 8}

= ⁵⁵²⁰⁰⁰/₅₅₂₀₀

= 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) = $6900

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

Simple Interest = $5520 (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 $6900

= ⁸/₁₀₀ × 6900

= ^{8 × 6900}/₁₀₀

= ⁵⁵²⁰⁰/₁₀₀ = 552

Thus, simple Interest for 1 year = $552

Now,

∵ If the simple Interest is $552, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₅₂ years

∴ If the simple Interest is $5520, then the time = ¹/₅₅₂ × 5520 years

= ^{1 × 5520}/₅₅₂ years

= ⁵⁵²⁰/₅₅₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) 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.

(2) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.

(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?

(4) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.

(6) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.

(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.

(8) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.