# Need help with interest (Nominal)

• Feb 27th 2010, 03:42 PM
krzyrice
Need help with interest (Nominal)
I need help with how to calculate nominal annual rate.

1) A sum of $850 is invested for 10 years and the interest is compounded quarterly. There is$1000 in the account at the end of 10 years. What is the nominal annual rate?

So to set this up is the equation:
1000 = 850(1+r/4)^(4*10) and we solve for r? I don't know if that equation is correct. But when I solve for it the answer comes out to be 0.0163 or 1.63%. Please confirm with me if that answer is correct.

2) An investment grows by 3% per year for 10 years. By what percent does it increase over the 10-year period?

Is the formula: P(1 + 0.03/1)^(1*10) and we are trying to find the effective rate. So should the answer be 34.39%?

3) If the balance, M, at time t in years, of a bank account that compounds its interest payments monthly is given by
M = M0(1.07763)^t
Note: In the M0, the 0 is a subscript.

What is the nominal annual rate?
Again I need help with nominal annual rate. In the back of the book it says the nominal annual rate is 7.5%. But I do not get how to find that answer. Please shed some light on this issue and help me with finding out how to solve this problem.

Thank you so much.
• Feb 27th 2010, 07:49 PM
Prove It
Quote:

Originally Posted by krzyrice
I need help with how to calculate nominal annual rate.

1) A sum of $850 is invested for 10 years and the interest is compounded quarterly. There is$1000 in the account at the end of 10 years. What is the nominal annual rate?

So to set this up is the equation:
1000 = 850(1+r/4)^(4*10) and we solve for r? I don't know if that equation is correct. But when I solve for it the answer comes out to be 0.0163 or 1.63%. Please confirm with me if that answer is correct.

2) An investment grows by 3% per year for 10 years. By what percent does it increase over the 10-year period?

Is the formula: P(1 + 0.03/1)^(1*10) and we are trying to find the effective rate. So should the answer be 34.39%?

3) If the balance, M, at time t in years, of a bank account that compounds its interest payments monthly is given by
M = M0(1.07763)^t
Note: In the M0, the 0 is a subscript.

What is the nominal annual rate?
Again I need help with nominal annual rate. In the back of the book it says the nominal annual rate is 7.5%. But I do not get how to find that answer. Please shed some light on this issue and help me with finding out how to solve this problem.

Thank you so much.

1. $\displaystyle A = P(1 + r)^t$.

Since this is being compounded quarterly for 10 years, there will be 40 time periods and the rate will be the rate every quarter.

So $\displaystyle 1000 = 850(1 + r)^{40}$

$\displaystyle \frac{20}{17} = (1 + r)^{40}$

$\displaystyle \left(\frac{20}{17}\right)^{\frac{1}{40}} = 1 + r$

$\displaystyle r = \left(\frac{20}{17}\right)^{\frac{1}{40}} - 1$.

This is the quarterly interest rate. So multiply by 4 to get the yearly interest rate.
• Feb 27th 2010, 07:55 PM
Prove It
Quote:

Originally Posted by krzyrice
2) An investment grows by 3% per year for 10 years. By what percent does it increase over the 10-year period?

Is the formula: P(1 + 0.03/1)^(1*10) and we are trying to find the effective rate. So should the answer be 34.39%?

Year 0: $\displaystyle A = P$

Year 1: $\displaystyle A = 1.03 \cdot P$

Year 2: $\displaystyle A = 1.03\cdot 1.03 \cdot P$

Year 3: $\displaystyle A = 1.03 \cdot 1.03 \cdot 1.03 \cdot P$.

Can you see that for year $\displaystyle n$ the amount will be

$\displaystyle A = 1.03^n\cdot P$.

So in 10 years: $\displaystyle A = 1.03^{10}\cdot P$

$\displaystyle \approx 1.3439 \cdot P$.

So it has increased by just over $\displaystyle 34.39\%$.
• Feb 28th 2010, 09:25 AM
krzyrice
Thank you so much. I got the same answers but wasn't sure if I did them right.