Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3812.5

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 = $3812.5 – $3050 = $762.5

Thus, Simple Interest = $762.5

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 × 762.5}/_{3050 × 5}

= ⁷⁶²⁵⁰/₁₅₂₅₀

= 5 years (using formula)

Thus, Time (T) = 5 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) = $3050

Rate of Simple Interest (R) = 5% per annum

Simple Interest = $762.5 (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 = 5% of Principal

= 5% of $3050

= ⁵/₁₀₀ × 3050

= ^{5 × 3050}/₁₀₀

= ¹⁵²⁵⁰/₁₀₀ = 152.5

Thus, simple Interest for 1 year = $152.5

Now,

∵ If the simple Interest is $152.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_152.5 years

∴ If the simple Interest is $762.5, then the time = ¹/_152.5 × 762.5 years

= ^{1 × 762.5}/_152.5 years

= ^762.5/_152.5 = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.

(2) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.

(4) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.

(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.

(7) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(8) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.

(10) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.