If you deposit $7,000 into a savings account with an annual interest rate of 5% annually...

If you deposit $7,000 into a savings account with an annual interest rate of 5% annually which is compounded monthly, What would be the value of the investment after 10 years?

Please show your work.

Expert Solution

Deposit : $7,000

Annual interest rate: 5% compounding monthly.

Time period : 10 Years

[When the interest compounds monthly basis, in such situation the total compounding periods becomes 12 in a year. Therefore, the time perios is multiplied by 12 and the interest rate is devided by 12]

Value of the investment after 10 years: Deposit * ( 1 + annual rate/12)^{Yearly time * 12}

Value of the investment after 10 years: $ 7,000 * ( 1 + 0.05/12)¹⁰ ^{* 12}

Value of the investment after 10 years: $ 7,000 * ( 1.00416)¹²⁰

Value of the investment after 10 years: $ 7,000 * 1.645641

Value of the investment after 10 years: $ 11,519.48

[Note: (1.00416)¹²⁰ can be calculated using dirty power method on calculator. To calculate the value of calculator follow these steps; (1) Press 1.00416, (2) then press √ symbol 12 times, (3) then press -1, (4) then multiply 120, (5) then press +1 , and at last (6) press * and = , 12 times.... Value on the calculator]

jeff jeffy answered 2 years ago

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