Simple Interest
Math MCQs

Question :    Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8100 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) = 10% per annum

Amount (A) = $8100

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 = $8100 – $4500 = $3600

Thus, Simple Interest = $3600

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 × 3600}/_{4500 × 10}

= ³⁶⁰⁰⁰⁰/₄₅₀₀₀

= 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) = 10% per annum

Simple Interest = $3600 (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 $4500

= ¹⁰/₁₀₀ × 4500

= ^{10 × 4500}/₁₀₀

= ⁴⁵⁰⁰⁰/₁₀₀ = 450

Thus, simple Interest for 1 year = $450

Now,

∵ If the simple Interest is $450, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₀ years

∴ If the simple Interest is $3600, then the time = ¹/₄₅₀ × 3600 years

= ^{1 × 3600}/₄₅₀ years

= ³⁶⁰⁰/₄₅₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?

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

(3) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?

(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?

(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?

(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?

(7) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?

(8) 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.

(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(10) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.