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Your grandfather put some money in an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money for the first time. The account currently has $3,996 in it and pays an 8% interest rate. a. How much money would be in the account if you left the money there until your 25th​ birthday? b. What if you left the money until your 65th​ birthday? c. How much money did your grandfather originally put in the​ account?

Respuesta :

Answer:

a.  $6,848.48

b.   $148,779.85

c. $1000

Explanation:

First we have to determine the present value of the money

The formula for calculating present value:

P = FV (1 + r)^-n

FV = Future value  

P = Present value  

R = interest rate  

N = number of years  

$3,996(1.08)^-18 = $1000

a. The formula for calculating future value:

FV = P x (1 + r) n

FV = Future value  

P = Present value  

R = interest rate  

N = number of years  

a. $1000 x (1.08)^25 = $6,848.48

b.  $1000 x (1.08)^65 = $148,779.85

Parrain

Based on the amount in the account and the interest rate, the following is true:

  • a. $6,848.44
  • b. $148,779.12
  • c. $1,000

The amount at your 25th birthday can be found as:

= Amount x ( 1 + rate) ^ number of years

Number of years:

= 25 - 18

= 7 years

Amount at 25th birthday:

= 3,996 x ( 1 + 8%)⁷

= $6,848.44

Amount at 65th birthday:

Number of years = 65 - 25

= 40 years

= 6,848.44 x ( 1 x 8%)⁴⁰

= $148,779.12

The amount that was originally deposited can be found from:

Amount at 18th birthday = Original amount x ( 1 x 8%)¹⁸

3,996 = Amount x 3.996019499

Amount = 3,996 / 3.996019499

= $1,000

In conclusion, $1,000 was initially deposited.

Find out more about future value at https://brainly.com/question/4473833.

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