At= P (1 + r/n) nt M =Prm / 1 – (1 + r m) – n M = log I/I0

Question

1. Suppose you deposit $10,000 in an account that paid 8% and was
compounded quarterly.

A) How much money would be in the account after 15 years?
B) How much money would be in the account if the account was
    compound daily instead of quarterly?

2. Suppose you took out a car loan for $15,000 @ 12% annual interest for 5
    years. What would your monthly payment be?

3. Suppose you invest $25,000 in an account that paid 6.5% and was
    compounded daily.

A) How long would it take for the money in the account to double?
B) How long would it take for the amount to reach $500,000?

4. If I = 108.3I0 for an earthquake, what is the magnitude of the earthquake?


Formulas:

At= P (1 + r/n) nt

M =Prm / 1 – (1 + r m) – n

M = log I/I0

Answer 1

1A)  $10,000 compounded quarterly at 8% for 15 years

       A = 10,000(1+.08/4)⁴⁽¹⁵⁾

       A = $32,810.31

1B)  $10,000 compounded daily at 8% for 15 years

      A = 10,000(1+.08/365)^365(15)

      A = $33,196.80

 

2)  Car loan $15,000 at 12% annual interest for 5 years.  Payment = ?

    

     Note:  Your formula wasn't clear so I looked this one up.

     In the formula rate = (monthly %)/1200

     M = P[rate + rate/[(1+rate)^months-1]]    rate = 12/1200 = 1/100 = .01

    

     M = 15000[.01 + [.01/[(1+.01)⁶⁰-1]

     M = $333.67

 

3A)  $25,000 compounded daily at 6.5%.  How long until A=$50,000?

      

       50,000 = 25,000(1+.065/365)^365t

       2 = (1+.065/365)^365t

       log2 = log(1+.065/365)^365t

       log2 = 365t[log(1+.065/365)]      

       t = log2/[365(log(1+.065/365)]

       t = 10.665 years

       t ≅ 10 years 8 months

 

3B)  $25,000 compounded daily at 6.5%.  How long until A=$500,000?

 

       500,000 = 25,000(1+.065/365)^365t

       20 = (1+.065/365)^365t

       log 20 = log (1+.065/365)^365t

       log 20 = 365t[log(1+.065/365)]

       t = log20/[365(log(1+.065/365)]

       t = 46.0923 years

       t = 46 years 1 month

 

4)  I = 108.310A₀   what is the magnitude?

     M = log(I/I₀)

     M = log (108.31I₀/I₀)

     M = log(108.31)

     M = 2.035