Mary just deposited $33,000 in an account paying 7% interest. She plans to leave the money in this account for eight years. How much will she have in the account at the end of the seventh year?
Mary and Joe would like to save up $10,000 by the end of three years from now to buy new furniture for their home. They currently have $1500 in a savings account set aside for the furniture. They would like to make three equal year end deposits to this savings account to pay for the furniture when they purchase it three years from now. Assuming that this account pays 6% interest, how much should the year end payments be?
Isabel deposits $6,000 into an account that earns 1.5% interest compounded monthly. Assuming no more deposits and no withdrawals are made, how much money is in the account after 4 years?
To calculate how much Mary will have in the account at the end of the seventh year, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after time t
P = the principal amount (initial deposit) = $33,000
r = annual interest rate (in decimal form) = 0.07
n = number of times interest is compounded per year (assuming it's compounded annually)
t = number of years = 7
Plug in the values into the formula:
A = 33000(1 + 0.07/1)^(1*7)
A = 33000(1 + 0.07)^7
Now, calculate the expression inside the parentheses first:
(1 + 0.07)^7 = 1.07^7
Using a calculator, evaluate 1.07^7 = 1.717
Now, substitute back in the formula:
A = 33000 * 1.717
A ≈ $56,721.00
Therefore, Mary will have approximately $56,721.00 in the account at the end of the seventh year.
For the second question about Mary and Joe saving $10,000 in three years, we can use the future value of an ordinary annuity formula:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = future value = $10,000
P = yearly payment
r = interest rate per year (in decimal form) = 0.06
n = number of years = 3
We need to solve for P, so rearrange the formula:
P = FV * r / [(1 + r)^n - 1]
Substitute the values:
P = 10000 * 0.06 / [(1 + 0.06)^3 - 1]
Using a calculator:
P ≈ $2951.22
Therefore, Mary and Joe should make yearly payments of approximately $2951.22 to reach their goal of saving $10,000 in three years.