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

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You know the interest, I, and you know the principle, P, and you know the time, t, which is 1 year. Solve for r, the interest rate. Remember that you need to convert the percentage to a decimal when you plug it into the formula.
  • #1
bap902
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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.

------

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.
 
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  • #2
bap902 said:

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.
bap902 said:
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.
bap902 said:
------

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.
bap902 said:
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.
bap902 said:
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.
 
  • #3
bap902 said:

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.
 

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

1. What is the difference between compound and simple interest rates?

The main difference between compound and simple interest rates is how the interest is calculated. Simple interest is based on the initial principal amount, while compound interest is calculated on the initial principal plus any accumulated interest. This means that with compound interest, the interest earned is added to the principal and then earns interest, resulting in a higher overall return compared to simple interest.

2. How is the interest rate determined for an investment?

The interest rate for an investment is determined by several factors, including the current market rates, the type of investment, and the risk associated with the investment. Higher-risk investments typically have higher interest rates to compensate for the increased risk, while lower-risk investments have lower interest rates.

3. What is the formula for calculating compound interest?

The formula for calculating compound interest is A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

4. How much interest will I earn on a $7,700 investment with a compound interest rate of 5% over 5 years?

Using the compound interest formula, the interest earned on a $7,700 investment with a 5% annual interest rate compounded annually for 5 years would be $2,177.63. This means the total amount after 5 years would be $9,877.63.

5. What are the advantages and disadvantages of compound interest?

The main advantage of compound interest is that it allows for a higher return on an investment compared to simple interest. However, the disadvantage is that it can also lead to higher debt if the interest is compounded on a loan or credit card balance. Additionally, compound interest may not always be beneficial if the interest rate is low or if the investment has a short term.

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