SOLUTION: 3. Use a financial calculator or computer software program to answer the following questions : A). What would be the future value of $ 19,378 invested now if the money rema

Question 1116427: 3. Use a financial calculator or computer software program to answer the following questions :
A). What would be the future value of $ 19,378 invested now if the money remains deposited for eight years, the annual interest rate is 18 percent, and the interest on the investment is compounded semi-annually?
B). How would your answer for (A) change if quarterly compounding were used?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
set present value = 19378
set number of time periods = 8 * 2 = 16
set interest rate per time period = 18/2 = 9%
set future value = 0
set payment per time period = 0
leave payments at end or beginning of time period alone since you are not doing payments.
click on future value to get future value = 76936.59

that was for semi-annual payments.
for quarterly payments, do the following:
set present value = 19378
set number of time periods = 8 * 4 = 32 *****
set interest rate per time period = 18/4 = 4.5% *****
set future value = 0
set pa7ment per time period = 0
leave payments at end or beginning of time period along since you are not doing payments.
click on future value to get future value = 79255.65

it is to be expected that the future value will be higher with quarterly compounding than with semi-annual compounding since you are earning interest on interest and the effective interest rate per year is higher.

with semi-annual compounding, your effective annual interest rate is (1 + .18/2) ^ 2 - 1 = .1881 * 100 = 18.81%.

with quarterly compounding, your effective annual interest rate is (1 + .18/4) ^ 4 - 1 = .192518601 * 100 = 19.2518601%.

the online calculator i used is at https://arachnoid.com/finance/

here are my inputs and outputs for semi-annual compounding.

$$$

here are my inputs and outputs for quarterly compounding.

$$$

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