If $32,500 is invested at 6.9% for 3 years. Find the future value if the interest is compounded the following ways:
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.
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
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.
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
Thank you all so much for the time you give, to help others. I appreciate it so much.
To find the future value of an investment with different compounding periods, we can use the formula for compound interest:
Future Value = Principal * (1 + (annual interest rate / number of compounding periods))^(number of compounding periods * number of years)
1. Annually:
In the case of annual compounding, the interest is added once a year. So, the number of compounding periods per year is 1. We can use the formula directly:
Future Value = $32,500 * (1 + (6.9% / 1))^(1 * 3)
2. Semiannually:
For semiannual compounding, the interest is added twice a year. The number of compounding periods per year is 2:
Future Value = $32,500 * (1 + (6.9% / 2))^(2 * 3)
3. Quarterly:
For quarterly compounding, the interest is added four times a year. The number of compounding periods per year is 4:
Future Value = $32,500 * (1 + (6.9% / 4))^(4 * 3)
4. Monthly:
For monthly compounding, the interest is added twelve times a year. The number of compounding periods per year is 12:
Future Value = $32,500 * (1 + (6.9% / 12))^(12 * 3)
5. Daily:
For daily compounding, the interest is added 365 times a year. The number of compounding periods per year is 365:
Future Value = $32,500 * (1 + (6.9% / 365))^(365 * 3)
6. Every minute (N-525,600):
We assume a year has 525,600 minutes. The number of compounding periods per year is 525,600:
Future Value = $32,500 * (1 + (6.9% / 525,600))^(525,600 * 3)
7. Continuously:
For continuous compounding, we use the formula for continuous interest:
Future Value = $32,500 * e^(6.9% * 3)
8. Simple:
For simple interest, we use the formula:
Future Value = Principal + (Principal * annual interest rate * number of years)
Now that we've explained how to set up the calculations for each case, you can substitute the values and evaluate the expressions to find the future values for each compounding period.