If you put $ 6,000 in a savings account that pays interest at the rate of 4 percent, compounded annually, how much will you have in five years? (Hint: Use the future value formula.) How much interest will you earn during the five years? If you put $ 6,000 each year into a savings account that pays interest at the rate of 4 percent a year, how much would you have after five years?
An investor in the 28 percent tax bracket is trying to decide which of two bonds to select: one is a 5.5 percent U. S. Treasury bond selling at par; the other is a municipal bond with a 4.25 percent coupon, which is also selling
To find out how much you will have in the savings account after five years with an interest rate of 4 percent compounded annually, you can use the future value formula:
FV = P(1 + r/n)^(nt)
Where:
FV = Future Value
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
Given:
Principal amount (P) = $6,000
Annual interest rate (r) = 4% or 0.04 (as a decimal)
Number of times compounded per year (n) = 1
Number of years (t) = 5
Using the formula, plug in the values:
FV = $6,000(1 + 0.04/1)^(1*5)
FV = $6,000(1.04)^5
FV ≈ $6,000(1.216653311)
FV ≈ $7,299.92
Therefore, you will have approximately $7,299.92 in the savings account after five years.
To calculate the interest earned during the five years, subtract the initial deposit amount (P) from the future value (FV):
Interest earned = FV - P
Interest earned = $7,299.92 - $6,000
Interest earned ≈ $1,299.92
Therefore, you will earn approximately $1,299.92 in interest over the five years.
If you were to put $6,000 each year into a savings account that pays 4 percent interest per year, the calculations will be slightly different. In this case, it is best to use the future value of an ordinary annuity formula:
FV = P * ((1 + r)^t - 1) / r
Where:
FV = Future Value
P = Annual deposit amount
r = Annual interest rate (as a decimal)
t = Number of years
Given:
Annual deposit amount (P) = $6,000
Annual interest rate (r) = 4% or 0.04 (as a decimal)
Number of years (t) = 5
Using the formula, plug in the values:
FV = $6,000 * ((1 + 0.04)^5 - 1) / 0.04
FV ≈ $6,000 * (1.216653311 - 1) / 0.04
FV ≈ $6,000 * 0.216653311 / 0.04
FV ≈ $32,799.92 / 0.04
FV ≈ $819,998
Therefore, you will have approximately $819,998 in the savings account after five years if you deposit $6,000 each year and earn a 4 percent interest rate per year.