a. The present value of $300 per year for 16 years at 6% is $3,031.77.
It is calculated using an online finance calculator as follows:
N (# of periods) = 16 years
I/Y (Interest per year) 6%
PMT (Periodic Payment) = 300
FV (Future Value) = $0
Results:
PV = $3,031.77
Sum of all periodic payments = $4,800.00
Total Interest $1,768.23
b. The present value of $150 per year for 8 years at 3% is $1,052.95.
It is calculated using an online finance calculator as follows:
(# of periods) = 8 years
I/Y (Interest per year) = 3%
PMT (Periodic Payment) = $150
FV (Future Value) = $0
Results:
PV = $1,052.95
Sum of all periodic payments = $1,200.00
Total Interest = $147.05
c. The present value of $700 per year for 8 years at 0% is $5,600.00.
It is calculated using an online finance calculator as follows:
N (# of periods) = 8 years
I/Y (Interest per year) = 0%
PMT (Periodic Payment) = $700
FV (Future Value) = $0
Results
PV = $5,600.00
Sum of all periodic payments = $5,600.00
d. The present value of $300 per year for 16 years at 6% as an annuity due is $3,213.67.
It is calculated using an online finance calculator as follows:
N (# of periods) = 16 years
I/Y (Interest per year) 6%
PMT (Periodic Payment) = 300
FV (Future Value) = $0
Results:
PV = $3,213.67
Sum of all periodic payments = $4,800.00
Total Interest = $1,586.33
e. The present value of $150 per year for 8 years at 3% as an annuity due is $1,084.54.
It is calculated using an online finance calculator as follows:
(# of periods) = 8 years
I/Y (Interest per year) = 3%
PMT (Periodic Payment) = $150
FV (Future Value) = $0
Results:
PV = $1,084.54
Sum of all periodic payments = $1,200.00
Total Interest = $115.46
f. The present value of $700 per year for 8 years at 0% as an annuity due is $5,600.
It is calculated using an online finance calculator as follows:
N (# of periods) = 8 years
I/Y (Interest per year) = 0%
PMT (Periodic Payment) = $700
FV (Future Value) = $0
Results
PV = $5,600.00
Sum of all periodic payments = $5,600.00
<h3>What is the difference between an ordinary annuity and an annuity due?</h3>
An ordinary annuity involves regular payments made <u>at the end</u> of each period, while an annuity due involves payments are made at the <u>beginning</u> of each period. For example, consistent quarterly stock dividends are an ordinary annuity just as monthly rent is an annuity due.
<h3>Data and Calculations:</h3>
a. $300 per year for 16 years at 6%
b. $150 per year for 8 years at 3%
c. $700 per year for 8 years at 0%
d. Present value of $300 per year for 16 years at 6%
e. Present value of $150 per year for 8 years at 3%
f. Present value of $700 per year for 8 years at 0%
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