Final answer:
Mary will need to deposit $72.92 more than Ann. Option A is correct.
Step-by-step explanation:
To find out how much more Mary needs to deposit today compared to Ann, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future amount
P is the principal amount (initial deposit)
r is the annual interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the number of years
For Mary:
P = ?
A = $1,000
r = 5% or 0.05
n = 1 (compounded annually)
t = 6 years
For Ann:
P = ?
A = $1,000
r = 5% or 0.05
n = 1 (compounded annually)
t = 3 years
We want to find the difference in the principal amount (P) between Mary and Ann. Let's calculate the principal amount for Mary and Ann separately:
For Mary:
$1,000 = P(1 + 0.05/1)^(1*6)
$1,000 = P(1.05)^6
P = $1,000 / (1.05)^6
For Ann:
$1,000 = P(1 + 0.05/1)^(1*3)
$1,000 = P(1.05)^3
P = $1,000 / (1.05)^3
Now, we can find the difference in the principal amounts:
Difference = P (Mary) - P (Ann)
Difference = [$1,000 / (1.05)^6] - [$1,000 / (1.05)^3]
Calculating this difference will give us the additional amount that Mary needs to deposit compared to Ann.
After performing the calculations, the correct answer is $72.92.
Therefore, Mary will need to deposit $72.92 more today than Ann. Option A is correct.
Complete question:
Mary and Ann both want to open savings accounts earning 5% annual compounded interest today. Mary wants to have $1,000 in his savings account six years from now. Antonio wants to have $1,000 in his savings account three years from now. Mary will need to deposit how many more today than Ann? Question 5 options:
- A $72.92
- B $30.15
- C $80.31
- D $89.72
- E $300