Simple Interest
Math MCQs

Question :    Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4500

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7020

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 = $7020 – $4500 = $2520

Thus, Simple Interest = $2520

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 × 2520}/_{4500 × 7}

= ²⁵²⁰⁰⁰/₃₁₅₀₀

= 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) = $4500

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2520 (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 = 7% of Principal

= 7% of $4500

= ⁷/₁₀₀ × 4500

= ^{7 × 4500}/₁₀₀

= ³¹⁵⁰⁰/₁₀₀ = 315

Thus, simple Interest for 1 year = $315

Now,

∵ If the simple Interest is $315, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₅ years

∴ If the simple Interest is $2520, then the time = ¹/₃₁₅ × 2520 years

= ^{1 × 2520}/₃₁₅ years

= ²⁵²⁰/₃₁₅ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.

(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?

(5) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?

(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?

(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.

(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?

(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.

(10) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.