Answer:
A(1) Future value of annual deposit = $4,345.97
A(2) Future value of semiannual deposit = $4,466.71
A(3) Future value of quarterly deposit = $4,530.15
B. The more frequent deposits and compounding of interest are, the higher the future value of an annuity of an annuity will be.
Explanation:
A(1). Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn if (1) $300 is deposited annually and the credit union pays interest annually.
These can be calculated using the Future Value (FV) of an Ordinary Annuity as follows:
FVA = P * (((1 + r)^n - 1) / r) ................................. (1)
Where,
FVA = Future value of the annual deposit = ?
P = Annual deposit = $300
r = Annual interest rate = 8%, or 0.08
n = number of years = 10
Substituting the values into equation (1), we have:
FVA = $300 * (((1 + 0.08)^10 - 1) / 0.08)
FVA = $4,345.97
A(2). Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn if (2) $150 is deposited semiannually and the credit union pays interest semiannually.
These can be calculated using the Future Value (FV) of an Ordinary Annuity as follows:
FVS = P * (((1 + r)^n - 1) / r) ................................. (2)
Where,
FVS = Future value of the semiannual deposit = ?
P = Semiannual deposit = $150
r = Semiannual interest rate = 8% / 2 = 0.08 / 2 = 0.04
n = number of semiannual = 10 * 2 = 20
Substituting the values into equation (2), we have:
FVS = $150 * (((1 + 0.04)^20 - 1) / 0.04)
FVS = $4,466.71
A(3). Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn if (3) $75 is deposited quarterly and the credit union pays interest quarterly.
These can be calculated using the Future Value (FV) of an Ordinary Annuity as follows:
FVQ = P * (((1 + r)^n - 1) / r) ................................. (3)
Where,
FVQ = Future value of the semiannual deposit = ?
P = Quarterly deposit = $75
r = Quarterly interest rate = 8% / 4 = 0.08 / 4 = 0.02
n = number of quarters = 10 * 4 = 40
Substituting the values into equation (3), we have:
FVQ = $75 * (((1 + 0.02)^40 - 1) / 0.02)
FVQ = $4,530.15
B. Use your finding in part a to discuss the effect of more frequent deposits and compounding of interest on the future value of an annuity.
Since the future value of quarterly deposit of $4,530.15 is greater than the future value of semiannual deposit of $4,466.71 which on its own is also greater than the future value of annual deposit of $4,345.97, this implies that the more frequent deposits and compounding of interest are, the higher the future value of an annuity will be.
