Question

2.- Cristina wishes to make a deposit of $50,000 in a financial institution, in order to continue making ten additional deposits every six months for an identical amount, where the first of them will be made within six months. If the financial institution offers and pays 10% every six months, how much will Cristina withdraw six months after the last deposit?

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Answer to a math question 2.- Cristina wishes to make a deposit of $50,000 in a financial institution, in order to continue making ten additional deposits every six months for an identical amount, where the first of them will be made within six months. If the financial institution offers and pays 10% every six months, how much will Cristina withdraw six months after the last deposit?

$Expert avatar$

Rasheed

4.7

110 Answers

To find out how much Cristina will withdraw six months after the last deposit, we need to calculate the future value of all deposits first.

The formula to calculate the future value of an ordinary annuity is:

FV = P \times \left( \dfrac{(1 + r)^n - 1}{r} \right)

where:
-

is the future value of the annuity
-

is the amount of each deposit
-

is the interest rate per period
-

is the total number of periods

Given:
-

P = $50,000

r = 10\% = 0.10

(interest rate per six months)
-

n = 20

(10 deposits every six months for a total of 20 periods)

Plugging in the values, we get:

FV = $50,000 \times \left( \dfrac{(1 + 0.10)^{20} - 1}{0.10} \right)

FV = $50,000 \times \left( \dfrac{(1.10)^{20} - 1}{0.10} \right)

Now, we calculate the future value:

FV = $50,000 \times \left( \dfrac{6.727499 - 1}{0.10} \right)

FV = $50,000 \times 57.27499

FV = $2,863,749.50

Therefore, Cristina will be able to withdraw $2,863,749.50 six months after the last deposit.

\boxed{Answer: $2,863,749.50}

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