Question
Deposits of $1 are made at the beginning of each year for 14 years. The annual effective interest rate is 3.5%. Calculate the accumulated value of the deposits on the date of the last deposit.
Answers
Answered by
GPT 3.5
To calculate the accumulated value of the deposits, we can use the formula for the future value of an annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value (accumulated value of the deposits)
P = Annual deposit amount
r = Annual interest rate
n = Number of years
In this case, P = $1, r = 3.5% = 0.035, and n = 14.
FV = $1 * [(1 + 0.035)^14 - 1] / 0.035
= $1 * [1.035^14 - 1] / 0.035
= $1 * [1.557407724 - 1] / 0.035
= $1 * 0.557407724 / 0.035
= $0.557407724 / 0.035
≈ $15.92
Therefore, the accumulated value of the deposits on the date of the last deposit is approximately $15.92.
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value (accumulated value of the deposits)
P = Annual deposit amount
r = Annual interest rate
n = Number of years
In this case, P = $1, r = 3.5% = 0.035, and n = 14.
FV = $1 * [(1 + 0.035)^14 - 1] / 0.035
= $1 * [1.035^14 - 1] / 0.035
= $1 * [1.557407724 - 1] / 0.035
= $1 * 0.557407724 / 0.035
= $0.557407724 / 0.035
≈ $15.92
Therefore, the accumulated value of the deposits on the date of the last deposit is approximately $15.92.