Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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

Amount (A) = $9350

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 = $9350 – $5500 = $3850

Thus, Simple Interest = $3850

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 × 3850}/_{5500 × 7}

= ³⁸⁵⁰⁰⁰/₃₈₅₀₀

= 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) = $5500

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

Simple Interest = $3850 (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 $5500

= ⁷/₁₀₀ × 5500

= ^{7 × 5500}/₁₀₀

= ³⁸⁵⁰⁰/₁₀₀ = 385

Thus, simple Interest for 1 year = $385

Now,

∵ If the simple Interest is $385, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₈₅ years

∴ If the simple Interest is $3850, then the time = ¹/₃₈₅ × 3850 years

= ^{1 × 3850}/₃₈₅ years

= ³⁸⁵⁰/₃₈₅ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.

(3) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?

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

(6) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.

(8) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(10) How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?