Respuesta :
Answer:
(a) 8.9 percent compounded monthly for five years is $2,503.32.
(b) 6.6 percent compounded quarterly for eight years is $2,310.09.
(c) 4.3 percent compounded daily for four years is $3,283.75.
(d) 5.7 percent compounded continuously for three years is $3,287.05
Explanation:
The Present Value is calculated by using:-
Present Value = Future Value / (1 + r)n
Here, r is the Interest Rate and 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
[tex]= $3,900 / (1 + 0.00741667)60\\= $3,900 / 1.5579298\\= $2,503.32[/tex]
(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
[tex]= $3,900 / (1 + 0.0165)32\\= $3,900 / 1.688248\\= $2,310.09[/tex]
(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
[tex]= $3,900 / (1 + 0.000117808)1460\\\\= $3,900 / 1.187665\\\\= $3,283.75[/tex]
(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
[tex]= $3,900 / (1 + 0.000156164)1095\\= $3,900 / 1.1864749\\= $3,287.05[/tex]
