Question

If a nominal interest rate of 10​% is compounded​ continuously, determine the unknown quantity in each of the following​ situations:

a. What uniform EOY amount for 11 years is equivalent to ​$8 comma 0008,000 at EOY 11​?

b. What is the present equivalent value of ​$900 per year for 15 ​years?

c. What is the future equivalent at the end of the fifth year of ​$246 payments made every six months during the five

​years? The first payment occurs six months from the present and the last occurs at the end of the fifth year.

d. Find the equivalent​ lump-sum amount at EOY nine when P0 =​$1,3001.

i=10%

Answer 1

EAR =[ e^(Annual percentage rate) -1]*100

10=(e^(APR%/100)-1)*100

APR% = 9.531

a

FVOrdinary Annuity = C*(((1 + i )^n -1)/i)

C = Cash flow per period

i = interest rate

n = number of payments

8000= Cash Flow*(((1+ 9.531/100)^11-1)/(9.531/100))

Cash Flow = 442.76

b

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 900*((1-(1+ 9.531/100)^-15)/(9.531/100))

PV = 7032.7

c

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

9.531 = ((1+Stated rate%/(2*100))^2-1)*100

Stated rate% = 9.3141

FVOrdinary Annuity = C*(((1 + i )^n -1)/i)

C = Cash flow per period

i = interest rate

n = number of payments

FV= 246*(((1+ 9.3141/200)^(5*2)-1)/(9.3141/200))

FV = 3045.08

d

Future value = present value*(1+ rate)^time

Future value = 13001*(1+0.1)^9

Future value = 30655.68