Question

1. A seven-year, $10,000 promissory note, dated May 1, 2007, with interest at 12% compounded quarterly is discounted four years after the date of issue at 16% compounded semi-annually. What are the proceeds of the note?

2. Find the nominal annual rate of interest compounded quarterly that is equal to an effective rate of 19.25%

3. $4,000 is due in five years. If money is worth 12% compounded annually, what is the equivalent payment in two years that would settle this debt?

4. A 3-year term deposit of $5,000 earns 8.5% compounded quarterly?

1. What is the maturity value?

2. How much interest did the deposit earn?

5. A deposit of $5,000 earns interest at 4% compounded semi-annually. After three-and-a-half years, the interest rate is changed to 4.5% compounded quarterly. How much is the account worth after 7 years?

6. Jan is saving for a new bike that will cost $800. She has $500, which she has invested at 7% compounded semi-annually. How many years will it be (approximately) until she has $800?

7. How long will it take for money to double if it is compounded quarterly at 6%?

Financial Mathematics

FORMULA SHEET

i = j / m

I = Prt

t = I / Pr

P = I / rt

S = P(1 + i)ⁿ

f = (1 + i)^m - 1

n = ln (S / P)

ln (1 + i)

Sn = R[(1 + p)ⁿ - 1]

p

R =          Sn

[(1 + p)ⁿ - 1] / p

14. = ln [1 + pSn/R] ln (1 + p)

Sn(due) = R[(1 + p)ⁿ - 1](1 + p)

p

n = ln [1 + [pSn(due) / R(1 + p)] ln(1 + p)

14. = -ln[1 - (p[1 + p]^dAn(def))/R] ln(1 + p)

An(def) = R [1 - (1 + p)^-n] p(1 + p)^d

A = R / p

m = j / i

S = P(1 + rt)

r = I / Pt

P = S / (1 + rt) = S(1 + i)^-n

c = # of compoundings/# of payments

p = (1 + i)^c - 1

i = [S / P] ^1/n - 1

An = R[1 - (1 + p)^-n]

p

R =          An

[1 - (1 + p)^-n] / p

14. = -ln [1 - pAn/R] ln (1 + p)

An(due) = R[1 - (1 + p)^-n](1 + p)

p

n = -ln[1 - [pAn(due) / R(1 + p)] ln(1 + p)

d = -ln{R[1-(1 + p)^-n] / pAn(def)} ln(1 + p)

Sn(def) = Sn

A(due) = (R / p)(1 + p)

Answer 1

You have asked multiple questions in a single post. Further one of your questions has multiple sub parts. I have addressed the first two questions completely. Please post the balance questions one by one, separately.

1. A seven-year, $10,000 promissory note, dated May 1, 2007, with interest at 12% compounded quarterly is discounted four years after the date of issue at 16% compounded semi-annually. What are the proceeds of the note?

Maturity value of seven year note = A x (1 + r)ⁿ = 10,000 x (1 + 12% / 4)^{(7 x 4)} = 10,000 x (1 + 3%)²⁸ = $ 22,879.28

This is discounted after 4 years, i.e. when there are three years to maturity. Hence, the proceeds of the note = Maturity value discounted by 3 years = 22,879.28 / (1 + i)^t = 22,879.28 / (1 + 16% / 2)^{(2 x 3)} = 22,879.28 / (1 + 8%)⁶ = $ 14,417.83

2. Find the nominal annual rate of interest compounded quarterly that is equal to an effective rate of 19.25%

Let r be the nominal annual rate. Then (1 + r / 4)⁴ = (1 + 19.25%)

Hence, r = 4 x [(1 + 19.25%)^1/4 - 1] = 18.00%