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Sagot :
Answer:
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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