finite math question

Question

. You have $10,000 to invest in a retirement savings account. Shakedown Investments offers a retirement account with 7.8% interest compounded monthly, while Robublind Associates offers a retirement account with 8.0% interest compounded semi-annually. If you’re thinking of investing this money for 6 years, which account gives you a better return? Why?

Answer 1

The formula for compound interest is:

 

I = P*{(1 + APR/n)^nt - 1}

 

Where:

I= the interest earned

P = the principle or initial investment = $10,000

APR = annual percentage rate expressed as a decimal = 0.07 for Shakedown and 0.08 for Robublind

n = number of compoundings per year = 12 for Shakedown and 2 for Robublind

t = years

 

For Shakedown:

 

I = ($10,000)*{(1 + 0.078/12)^12*6 - 1}

I = ($10,000)*{(1.0065)⁷² - 1}

 

For Robulind:

 

I = ($10,000)*{(1 + 0.08/2)2*6 - 1}

I = ($10,000)*{(1.04)¹² - 1}

 

Compute the interest earned from each firm to determine the better return.

Answer 2

Compound interest uses the formula:

A = P (1+r/n)^nt

 

P is the initial investment

A is the final amount

r is the interest rate, as a decimal

n is the number of times compounded per year

t is the number of years

 

For your problem, you're comparing two situations, and want to know which has a higher final amount.

 

Shakedown:

r = 7.8% = 0.078

n = 12

 

Robublind:

r = 8.0% = 0.08

n = 2

 

Both have the same time and principal

P = $10,000

t = 6 yrs

 

Plug each set of values in to the formula, and figure out which one is higher.