Sally plans to retire at the age of 64 and has an account that will provide 6% interest compounded monthly. Determine how much money needs to be in Sally's account on the day sure turns 64 if she would like to be able to receive monthly payments of $9500 from age 64 until age 83.

She needs to have $694,700 in her account

Step-by-step explanation:

Here, we want to know the amount that should be in Sally’s account on that day she turns 64

Firstly, we need to know the difference between the ages of 64 and 83

The difference between these ages are 83-64 = 19

So, she intends receiving $9,500 per month for 19 years

The number of months in 19 years is 19 * 12 = 228 months

So, the total amount of money she needs is 228 * 9,500 = $2,166,000

Now, we have an interest that would be compounded but in this case, we already have the amount needed but what we need is the principal to be compounded in this case

The formula for compound interest here is;

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

where A is the amount which is 2,166,000

P is ?

r is the interest rate = 6% = 6/100 = 0.06

n is the number of times we are compounding in a year; since it is monthly, that would be 12 times in a year

t is the number of years which is 19 in this case

Substituting all values, we have that;

2,166,000 = P( 1 + 0.06/12)^(12*19)

2,166,000 = P(1.005)^(228)

P = 2,166,000/(1.005)^228

P = $694,699

This rounded to a whole dollar is P = $694,700

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step-by-step explanation:

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