Find the present value needed to have $ 1.00 compounded quarterly for 5 years at 6% using the formula
(a) 74 ¢ (b) 75 ¢ (c) 76 ¢ (d) 77 ¢ (e) 78 ¢
To calculate the present value needed to have $1.00 compounded quarterly for 5 years at 6%, we can use the formula for compound interest:
PV = FV / (1 + r)^n
Where:
- PV is the present value
- FV is the future value ($1.00 in this case)
- r is the interest rate per compounding period (6% divided by 4 as it is compounded quarterly)
- n is the number of compounding periods (5 years multiplied by 4 since it is compounded quarterly).
Let's calculate it step by step:
PV = $1.00 / (1 + (0.06/4))^(5*4)
= $1.00 / (1 + 0.015)^(20)
= $1.00 / (1.015)^(20)
= $1.00 / 1.348608
Now, let's calculate the division:
PV = 0.7413 (approximated to four decimal places)
Therefore, the present value needed to have $1.00 compounded quarterly for 5 years at 6% is approximately 74 cents. Hence, the correct answer is (a) 74 ¢.