Tiffany invested $725 at the end of every month in an investment fund that was earning interest at a rate of 4.74% compounded monthly. She stopped making regular deposits at the end of 10 years when the interest rate changed to 6.69% compounded quarterly. However, she let the money grow in this investment fund for the next 2 years.
a. Calculate the accumulated balance in her investment fund at the end of 10 years.
To calculate the accumulated balance in Tiffany's investment fund at the end of 10 years, we need to calculate the future value of the monthly deposits she made plus the growth of the fund over the 10-year period.
First, let's calculate the future value of Tiffany's monthly deposits using the future value of an ordinary annuity formula:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value
P = Monthly deposit amount ($725)
r = Interest rate per period (4.74% / 12 = 0.00395)
n = Number of periods (10 years * 12 months = 120 months)
FV = 725 * ((1 + 0.00395)^120 - 1) / 0.00395 ≈ $103,452.17
So, the future value of Tiffany's monthly deposits after 10 years is approximately $103,452.17.
Next, let's calculate the additional growth of the fund over the 10-year period. Since the interest rate changed to 6.69% compounded quarterly, we can use the following formula to calculate the future value:
FV = P * (1 + r/n)^(n*t)
Where:
FV = Future Value
P = Principal amount (current balance after 10 years = $103,452.17)
r = Interest rate per period (6.69% / 4 = 0.016725)
n = Number of compounding periods per year (quarterly compounding = 4)
t = Number of years (2 years)
FV = 103452.17 * (1 + 0.016725/4)^(4*2) ≈ $117,828.14
So, the accumulated balance in Tiffany's investment fund at the end of 10 years is approximately $117,828.14.
To calculate the accumulated balance in Tiffany's investment fund at the end of 10 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated balance
P = Principal amount (monthly contribution)
r = Annual interest rate (expressed as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, Tiffany invested $725 at the end of every month for 10 years, so the principal amount, P, is $725. The annual interest rate, r, is 4.74% or 0.0474 as a decimal. The interest is compounded monthly, so n is 12 (monthly compounding) and t is 10 (number of years).
Plugging in these values into the formula, we get:
A = 725(1 + 0.0474/12)^(12*10) = $13,610.04
Therefore, the accumulated balance in Tiffany's investment fund at the end of 10 years is $13,610.04.