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Suppose you deposit 1000 ​$ in a savings account that pays interest at an annual rate of ​4%. If no money is added or withdrawn from the​ account, answer the following questions.

How much will be in the account after 3 ​years?
b. How much will be in the account after 16 ​years?
c. How many years will it take for the account to contain 1,500 ​$​?
d. How many years will it take for the account to contain 2000​$​?


Some one please helppppppp mee

User BoshWash
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2 Answers

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Final answer:

To determine the future value of a savings account with 4% annual interest, compound interest calculations are used. After 3 years, the account will have approximately $1124.86, and after 16 years, $1809.48. It will take roughly 10.67 years to reach $1500, and about 17.67 years to accumulate $2000.

Step-by-step explanation:

The student is asking about the future value of a savings account with an interest rate of 4% compounded annually. To calculate the amount in the account after a certain number of years, the formula for compound interest is used:

A = P(1 + r/n)^(nt)

Where:

  • A = the future value of the investment/loan, including interest
  • P = the principal investment amount (initial deposit)
  • r = the annual interest rate (decimal)
  • n = the number of times that interest is compounded per year
  • t = the number of years the money is invested or borrowed for

Assuming the interest is compounded once a year (n = 1), the following calculations can be made:

a. Amount after 3 years:

A = $1000 * (1 + 0.04/1)^(1*3) = $1000 * (1.04)^3 = $1124.86

b. Amount after 16 years:

A = $1000 * (1.04)^16 = $1809.48

c. Years to contain $1500:

1500 = $1000 * (1.04)^t

t = ln(1500/1000) / ln(1.04) ≈ 10.67 years

d. Years to contain $2000:

2000 = $1000 * (1.04)^t

t = ln(2000/1000) / ln(1.04) ≈ 17.67 years

User Ian Knight
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8.4k points
3 votes

Answer:

a. 1124.86

b. 1872.98

c. 10.35

d. 17.7

Step-by-step explanation:

use the formula A(t) = a (1+r)^t

User VanHoesel
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8.6k points

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