Finance Problems: Compound and Simple Interest Rates for $7,700 Investment

[bap902]

Homework Statement

Compute the compound amount after 1 year for $7,700 invested at 8% interest compounded quarterly. What simple interest rate will yield the same amount in 1 year? (Round your answer to 2 decimal places.)

2. The attempt at a solution
I did this on my calculator so...

N=4
I%=8
PV=7700
PMT=0
FV=8334.727632
P/Y=4
C/Y=4

The amount compounded in the year is 8334.727632-7700=634.727632. Is that first part right? If so, I still don't know how to get the simple interest rate after finding out the amount compounded.

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Homework Statement

In 3 years, Jim wants to have $22,090 to buy a new car. How much must Jim save each month if the interest rate is 6% compounded monthly? How much of the $22,090 does Jim actually deposit and how much of it is interest?

2. The attempt at a solution
I figured out that Jim must save $561.5705983 per month. Using the calculator:

N=36
I%=6
PV=0
PMT=$561.5705983
FV=22090
P/Y=12
C/Y=12

I'm not sure how to find out how much he actually deposited and how much of it is interest.

 

[Mark44]

Homework Statement

Compute the compound amount after 1 year for $7,700 invested at 8% interest compounded quarterly. What simple interest rate will yield the same amount in 1 year? (Round your answer to 2 decimal places.)

2. The attempt at a solution
I did this on my calculator so...

N=4
I%=8
PV=7700
PMT=0
FV=8334.727632

The number above is basically the compound amount; you just need to round it to the nearest cent.

P/Y=4
C/Y=4

The amount compounded in the year is 8334.727632-7700=634.727632. Is that first part right? If so, I still don't know how to get the simple interest rate after finding out the amount compounded.

The $634.73 is your interest. The formula for simple interest is I = Prt. The only thing you don't know in this formula is the interest rate. You have already calculated I, the interest, and you know the amount invested, P, and the time, 1 year.

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Homework Statement

In 3 years, Jim wants to have $22,090 to buy a new car. How much must Jim save each month if the interest rate is 6% compounded monthly? How much of the $22,090 does Jim actually deposit and how much of it is interest?

This is an annuity problem, where an investment of a certain size is made each month. You need a formula for this unless the goal is for you to derive a formula.

2. The attempt at a solution
I figured out that Jim must save $561.5705983 per month. Using the calculator:

You said "using the calculator" but I have no idea what you did with your calculator.

N=36
I%=6
PV=0
PMT=$561.5705983
FV=22090
P/Y=12
C/Y=12

I'm not sure how to find out how much he actually deposited and how much of it is interest.

 

[Anakin_k]

Homework Statement

Compute the compound amount after 1 year for $7,700 invested at 8% interest compounded quarterly. What simple interest rate will yield the same amount in 1 year? (Round your answer to 2 decimal places.)

2. The attempt at a solution
I did this on my calculator so...

N=4
I%=8
PV=7700
PMT=0
FV=8334.727632
P/Y=4
C/Y=4

The amount compounded in the year is 8334.727632-7700=634.727632. Is that first part right? If so, I still don't know how to get the simple interest rate after finding out the amount compounded.

Your final compounded value is incorrect. The answer is about $10475.76.
Now that you have the compounded value, you can see that the interest you earn in that one year is $10475.76-7700=$2775.76. I will leave it up to you to try the formula FV = PV (1+i)^n to find the answer that I got. Remember i is the interest rate (not in %) and n is the number of periods. In one year, you would have 4 periods if the interest is compounded quarterly.

Now use I = Prt.