Question

Suppose you deposit $1500 in a savings account that pays interest at an annual rate of 6% if no money is added or withdrawn from the account answer the following questions how much will be in the account in four years how much will be in the account after 16 years how many years will it take for the account to contain $2000 How many years will it take for the account to contain $2500

Answer 1

Answer:

In 4 years = $1,893.72

In 16 years = $3,810.53

years to contain $2,000 = 4.9371454128

years to contain $2,500 = 8.766692911

Step-by-step explanation:

In 4 years

A = 1,500 (1 + 0.06)^4

  = $1,893.72

In 16 years

A = 1,500 (1 + 0.06)^16

   = $3, 810.53

to find number of years

t = ln (A/P) / ln (1+r)

when A = 2,000

t = ln(2,000/1,500) / ln(1+0.06)

 = 4.9371454128 years

when A = 2,500

t = ln(2,500/1,500) / ln(1+0.06)

 = 8.766692911 years

PS: You can also use log in place of ln

Answer 2

The number of years it will take for the account to contain $2000 is 4.94 years while it will take 8.77 years to contain $2500.

Calculation of future value and the number of years it takes

Let:

PV = Present value = $1,500

r = Interest rate = 6%, or 0.06

n = number of years

FVn = Future value after a certain number of years

Therefore, we have:

The amount that will be in the account in four years can be calculated using the future value (FV) formula as follows:

FV4 = PV * (1 + r)^n = $1,500 * (1 + 0.06)^4 = $1,893.72

Therefore, the amount that will be in the account in four years is $1,893.72.

The amount that will be in the account after 16 years can also be calculated using the future value (FV) formula as follows:

FV16 = PV * (1 + r)^n = $1,500 * (1 + 0.06)^16 = $3,810.53

Therefore, the amount that will be in the account after 16 years is $3,810.53.

The number of years will it take for the account to contain $2000 can be calculated using the following formula:

n = (log(FV/PV)) / (log(1+r)) = (log($2,000/$1,500)) / (log(1+0.06)) = 0.1249387366083 / 0.0253058652647703 = 4.94 years

Therefore, the number of years it will take for the account to contain $2000 is 4.94 years.

The number of years it will take for the account to contain $2500 can be calculated using the following formula:

n = (log(FV/PV)) / (log(1+r)) = (log($2,500/$1,500)) / (log(1+0.06)) = 0.221848749616356 / 0.0253058652647703 = 8.77 years

Therefore, the number of years it will take for the account to contain $2000 is 8.77 years.

Learn more about future value here: https://brainly.com/question/13504821.

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