1. The future value is $334,804.
2. The present value is $68,369.
3. The future value as of the end of the 16th period is $79,035.
4. The present value is $19,024.
Future and Present Value Calculations:
1. Future Value:
The future value (FV) of 22 periodic payments of $5,590 each, made at the beginning of each period and compounded at 8%, can be calculated using the formula:
FV = Pmt * ((1 + r)^n - 1) / r
where:
Pmt = Payment amount ($5,590)
r = Interest rate per period (8% / 12 = 0.67%)
n = Number of periods (22)
Plugging in the values:
FV = 5590 * ((1 + 0.0067)^22 - 1) / 0.0067
FV ≈ $334,804
Therefore, the future value is $334,804.
2. Present Value:
The present value (PV) of $3,670 to be received at the beginning of each of 28 periods, discounted at 5% compound interest, can be calculated using the formula:
PV = Pmt / (1 + r)^n
where:
Pmt = Payment amount ($3,670)
r = Discount rate per period (5% / 12 = 0.42%)
n = Number of periods (28)
Plugging in the values:
PV = 3670 / (1 + 0.0042)^28
PV ≈ $68,369
Therefore, the present value is $68,369.
3. Future Value:
The future value of 16 deposits of $3,050 each made at the beginning of each period and compounded at 10% can be calculated using the same formula as question 1:
FV = 3050 * ((1 + 0.1)^16 - 1) / 0.1
FV ≈ $79,035
Therefore, the future value as of the end of the 16th period is $79,035.
4. Present Value:
The present value of 7 receipts of $3,130 each received at the beginning of each period, discounted at 9% compound interest, can be calculated using the formula:
PV = Pmt / (1 + r)^n
where:
Pmt = Payment amount ($3,130)
r = Discount rate per period (9% / 12 = 0.75%)
n = Number of periods (7)
Plugging in the values:
PV = 3130 / (1 + 0.0075)^7
PV ≈ $19,024
Therefore, the present value is $19,024.
The Complete Question
1. What is the future value of 22 periodic payments of $5,590 each made at the beginning of each period and compounded at 8% ? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)
The future value $______
2. What is the present value of $3,670 to be received at the beginning of each of 28 periods, discounted at 5% compound interest? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.) The present value $_____
3. What is the future value of 16 deposits of $3,050 each made at the beginning of each period and compounded at 10% ? (Future value as of the end of the 16th period.) (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.
The future value $ ______
4. What is the present value of 7 receipts of $3,130 each received at the beginning of each period, discounted at 9% compounded interest? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.) The present value $________