If $32,500 is invested at 6.9% for 3 years. Find the future value if the interest is compounded the following ways:

Question

annually, semiannually, quarterly, monthly, daily, every minute (N-525,600), continuously, and simple (not compounded. I don't know to set this up or how to start it. If you can help Thank you and it is appreciated.

Answer 1

a) annually

A = p(1+ r)^t
A = 32500(1+ 0.069)^3
A = 32500(1 .069)^3
A = $39,702.37

b) semiannually

A = p(1+ r/n)^tn
A = 32500(1 + 0.069/2)^(3*2)
A = 32500(1.0345)^6
A = $39,835.14

c) quarterly

A = p(1+ r/n)^tn
A = 32500( 1+ 0.069/4)^(3*4)
A = 32500(1.01725)^12
A = $39,903.94

d) Monthly

A = p(1+ r/n)^tn
A = 32500(1 + 0.069/12)^(12*3)
A =32500(1.00575)^36
A = $ 39,950.74

e) Daily

A = p(1+ r/n)^tn
A = 32500(1+ .069/365)^(3*365)
A = $39,973.65

f) every minute

A = p(1 + r/n)^tn
A= 32500( 1+ 0.069/525600)^(525600*3)
A = $39,974.43

g) Continuously

A = pe^rt
A = 32500e^(0.069*3
A = 32500e^0.207
A = $ 39,974.43

h) Simple (not compound)

A = p(1+ r)^t
A = 32500( 1+ 0.069)^3
A = 32500( 1.069)^3
A = $ 39,702.37

Answer 2

in each case you divide the rate by the annual compounding frequence,
and multiply the years by that annual compouding frequency
e.g. if compounded quarterly, the annual compounding frequencey is 4

I will do that one, you try the others.

6.9 %>
compounded quarterly
i = .069/4 = .01725
n = 3(4) = 12

Amount = 32500( 1 + .01725)^12
= 32500 (1.01725)^12 = $39,903.94

for continuous, you use the formula

amount = principal x e^(rate x time)
= 32500 e^(.069(3))
= $39,974.43

For simple interest:
amount = 32500 + 32500(.069)(3) = $39,227.50

Give the others a good try.

Answer 3

There is typo for simple interest
Simple interest. =Prt
= 32500(.069)(3)
=$6,727.50

Amount. = p + interest
A = $ 32500 + $6727.50
A = 39,227.50

Answer 4

Thank you all so much for the time you give, to help others. I appreciate it so much.