Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4100

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $7380

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 = $7380 – $4100 = $3280

Thus, Simple Interest = $3280

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 × 3280}/_{4100 × 10}

= ³²⁸⁰⁰⁰/₄₁₀₀₀

= 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) = $4100

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3280 (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 $4100

= ¹⁰/₁₀₀ × 4100

= ^{10 × 4100}/₁₀₀

= ⁴¹⁰⁰⁰/₁₀₀ = 410

Thus, simple Interest for 1 year = $410

Now,

∵ If the simple Interest is $410, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₀ years

∴ If the simple Interest is $3280, then the time = ¹/₄₁₀ × 3280 years

= ^{1 × 3280}/₄₁₀ years

= ³²⁸⁰/₄₁₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?

(2) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.

(3) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.

(4) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.

(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?

(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?

(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(9) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?