+0

# Future value questions

0
60
2

Hello so I recently started a math course and need some help, not with necessarily finding the answers but with making sure the way im doing the formula is correct. The question im having the most issue with and second guessing is as follows: Brianna deposits \$150 at the end of each quarter into an account that pays 8% compounded quarterly. Calculate the amount in the account at the end of 20.5 years.

So the formula is as follows
FV= R [( 1+ i) ^n -1] / i

the formula completed is this
FV= 150 [( 1+ .08/4) ^ 82 -1] / i

.08/4=.02 ( i )
.02 + 1 = 1.02
20.5 x 4=82 (n)
1.02 ^ 82 = 5.072406898
5.072406898 - 1 = 4.072406898
4.072406898 / .02 = 203.6203449

203.6203449 * 150 = 30543.05174

30543.05174 seems rather high so i'm afraid im just either misreading the question or have somehow screwed up a portion of the equation.

Note: This is just the portion for learning how to calculate the future value, present value is my next unit but I want to try and get as many correct answers while understanding the formula as best I can. Thankyou in advance for any help

Jul 11, 2023

#1
0

1 - Your calculations are correct.

2 - One thing you must always remember: the interest rate MUST always match the periodic payments. Examples: if the payments are made monthly, then the interest rate must be compounded monthly. Or, if the payments are semi-annual, then the interest rate must be compounded semi-annually.... and so on.

3 - You must learn how to convert interest rate from one compounding period to another. Examples: convert 8% effective annual rate to an equivalent rate compounded quarterly: solution: 1.08 =1.08^(1/4)=1.01942655 - 1  x  4  x  100=7.7706% compounded quarterly=8% effective annual rate.

4 - You should access to a financial calculator to verify your calculations such as this one, which is very good:

http://arachnoid.com/finance/index.html

5 - Read the instructions on that site and learn how to use it. If you use correctly, it will always give you correct answers. Good luck to you.

Jul 11, 2023
#2
+8
0