Question

Find the present value of $3,900 under each of the following rates and periods: (Round your final answer to the nearest penny.) a. 8.9 percent compounded monthly for five years. Present value $ b. 6.6 percent compounded quarterly for eight years. Present value $ c. 4.3 percent compounded daily for four years. Present value $ d. 5.7 percent compounded continuously for three years. Present value $

Answer 1

The Present Value is calculated by using the following formula

Present Value = Future Value / (1 + r)ⁿ

Where, “r” is the Interest Rate & “n” is the number of periods

(a). 8.9 percent compounded monthly for five years

Future Value = $3,900

Interest Rate (r) = 0.741667% [8.90% / 12 Months])

Number period (n) = 60 Years [5 Years x 12]

Present Value = Future Value / (1 + r)n

= $3,900 / (1 + 0.00741667)⁶⁰

= $3,900 / 1.5579298

= $2,503.32

(b). 6.6 percent compounded quarterly for eight years

Future Value = $3,900

Interest Rate (r) = 1.65% [6.60% / 4]

Number period (n) = 32 Years [8 Years x 4]

Present Value = Future Value / (1 + r)n

= $3,900 / (1 + 0.0165)³²

= $3,900 / 1.688248

= $2,310.09

(c). 4.3 percent compounded daily for four years

Future Value = $3,900

Interest Rate (r) = 0.0117808% [4.30% / 365 Days]

Number period (n) = 1460 Years [4 Years x 365 Days]

Present Value = Future Value / (1 + r)n

= $3,900 / (1 + 0.000117808)¹⁴⁶⁰

= $3,900 / 1.187665

= $3,283.75

(d). 5.7 percent compounded continuously for three years

Future Value = $3,900

Interest Rate (r) = 0.0156164% [5.70% / 365 Days]

Number period (n) = 1095 Years [3 Years x 365 Days]

Present Value = Future Value / (1 + r)n

= $3,900 / (1 + 0.000156164)¹⁰⁹⁵

= $3,900 / 1.1864749

= $3,287.05