Question

1. Jake borrowed $6,500 for 18 months at 5.05%. How much interest will he pay?

2. Sarah borrowed $1,000 on March 12, 2007 and repaid it on September 4, 2010. For how many days was the loan outstanding?

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3. A loan of $1,100 can be repaid in 8 months by paying the principal sum borrowed plus $44 in interest. What was the rate of interest charged?

4. How many days would it take for $1,500 to earn $20.96 at 8.5%?

5. What amount of money would earn $54.69 in 3 months at 8.75%?

6. Helen borrowed $500 at 4% from her Mom on April 4, and promised to repay the money in 90 days.

1. What is the due date?

2. How much will she owe her Mom on that date?

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7. Dave borrowed money from Steve at 8% for 9 months. He now owes Steve $424. How much did be borrow?

8. Debt payments of $600 each are due 3 months and 6 months from now respectively. If interest is at 10%, what single payment is required to settle the debt today?

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

n = 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)

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

Sn(def) = Sn

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

Answer 1

Jake borrowed $6,500 for 18 months at 5.05%. How much interest will he pay?

Interest = Prt = 6,500 x 5.05% x 18 / 12 = $ 492.375

Sarah borrowed $1,000 on March 12, 2007 and repaid it on September 4, 2010. For how many days was the loan outstanding?

Outstanding days = Sep 4, 2010 - Mar 12, 2007 = 1,272 days

A loan of $1,100 can be repaid in 8 months by paying the principal sum borrowed plus $44 in interest. What was the rate of interest charged?

Rate of interest = I / Pt = 44 / (1,100 x 8 / 12) = 6%

4. How many days would it take for $1,500 to earn $20.96 at 8.5%?

t = I / Pr = 20.96 / (1,500 x 8.5%) x 365 = 60 days

5. What amount of money would earn $54.69 in 3 months at 8.75%?

P = I / rt = 54.69 / (8.75% x 3 / 12) = $ 2,500

Helen borrowed $500 at 4% from her Mom on April 4, and promised to repay the money in 90 days.
What is the due date?

Due date = April 4 + 90 days = July 4

How much will she owe her Mom on that date?

Amount owed = P x (1 + rt) = 500 x (1 + 4% x 90 / 365) = $ 504.93

Dave borrowed money from Steve at 8% for 9 months. He now owes Steve $424. How much did be borrow?

Amount = 424 = P x (1 + rt) = P x (1 + 8% x 9 / 12)

Hence, P = 424 / (1 + 8% x 9 / 12) = $ 400

Debt payments of $600 each are due 3 months and 6 months from now respectively. If interest is at 10%, what single payment is required to settle the debt today?

Single payment required to settle the debt today = 600 / (1 + 10% x 3 / 12) + 600 / (1 + 10% x 6 / 12) = $ 1156.79