Answer:
a. Amount = $1653.93
b. Amount = $1835.82
Explanation:
a.
The Present Value is the deposited amount of future payments.
The payments are annuity if they are made at the end of each year.
To compute the present value of an annuity with periodic payment, we'll make use of the following formula:
M(1 - (1 + r)^- T)/ r
Where
M = Periodic Payment = $230
T = Periods = 15
r = rate = 11% = 0.11
So, Amount of Deposit = 230(1 - (1 + 0.11)^-15)/0.11
Amount = 230(1 - (1.11)^-15)/0.11
Amount = 230 ( 1 - 0.209)/0.11
Amount = 230 * 0.791/0.11
Amount = 230 * 7.191
Amount = $1653.93
b.
In this case payments are made at the beginning of each period
This means that the payments are an annuity due.
To compute the present value of an annuity due with periodic payment, we'll make use of the following formula
M((1 + r) - ( 1 + r) ^ ( 1 - T))/r
Amount = 230(( 1 + 0.11) - (1 + 0.11) ^ (1 - 15))/0.11
Amount. = 230((1.11 - 1.11^-14))/0.11
Amount = 230(1.11 - 0.232)/0.11
Amount = 230 * 0.878/0.11
Amount = 201.94/0.11
Amount = $1835.82
