Question

Stereo Inc. sells a stereo system for $600 down and monthly payments of $40 for the next 4 years. If the interest rate is 3.25% per month, find:
a) The cost of the stereo.
Answer = $
Hint: Make sure you are using the MONTHLY interest rate, meaning 3.25 % is APR/12.

Answer 1

First you need to find how many months in 4 years. That equals 4x12 which is 48. 48 payments of 40 dollars with 3.25% interest per year + 600 dollars down.

The formula for compound interest is FV = PV × (1+r)^n where FV = Future Value PV = Present Value r = annual interest rate n = number of periods

n=48
PV= 40
r= 0.0325 (3.25%)

FV = 40 * (1+0.0325)^48

FV = 40 * (1.0325)^48

FV = 40 * 4.64218982962

FV = 185.687593185

FV = $185.69

(185.69 + 40)/2 = mean (average) payment
112.84 = average payment

48 * 112.84 = 5416.32

5416.32+600= $6016.32

So your final answer is "The stereo costs $6016.32 total"

Please appreciate this... it took me almost 10 minutes cause I kept on confusing simple interest with compound interest.

Answer 2

Thank you I do appreciate, but it says my answer is wrong

Answer 3

meh. sorry

Answer 4

Can you help me with this one: what annual rate of interest compounded annually is required to double an investment in 14 years. The answer I am getting is 5.1% and its wrong

Answer 5

FV must equal 2PV which makes it pretty easy. All we have to do is make sure that (1+r)^n is equal to 2. Since we know what the number of periods is we know that FV = PV x (1+r)^14
The future and present values themselves don't matter but their proportion does. Lets just say they are 4 and 2.
4 = 2 x (1+r)^14
We need to find out what to the fourteenth power equals two. To do this we can use a root calculator and find the 14th root of 2. The answer comes to about 1.05075663865. we subtract 1 from this and get 0.05075663865. It appears you are correct in saying it it about 5.1%. Try rounding it to 5.08%. Make sure you know where they want you to round to.