Answer:
a) The amount that could be withdrawn at t = 10 is $68,872.
b) The uniform annual series of deposits is $3,925.
Explanation:
a) What amount could be withdrawn at t = 10? $ Round entry to the nearest dollar. Tolerance is ±4.
Note: See the attached excel for the calculation of the future value in year 10.
From the attached excel file, we have:
Future value in year 10 = $68,872
Therefore, the amount that could be withdrawn at t = 10 is $68,872.
b) What uniform annual series of deposits (n = 10) would result in the same accumulated balance at the end of year 10? $ Round entry to the nearest dollar. Tolerance is ±4.
To calculate the uniform annual series of deposits, we use the formula for calculating the future value of ordinary annuity for as follows:
FV = M * (((1 + r)^n - 1) / r) ................................. (1)
Where,
FV = Future value of the amount deposited in after 10 years = $68,872
M = Uniform annual series of deposits = ?
r = Interest rate = 12%, or 0.12
n = number of year = 10 years
Substituting the values into equation (1) and solve for M , we have:
$68,872 = M * (((1 + 0.12)^10 - 1) / 0.12)
$68,872 = M * 17.5487350695351
M = $68,872 / 17.5487350695351
M = $3,925
Therefore, the uniform annual series of deposits is $3,925.
