1. A bank account has an interest rate of 1.8%. What is the equivalent interest rate used when…
a) compounding monthly? b) compounding quarterly?
c) compounding weekly? d) compounding daily?
2. Mike invests $10 000 at 6% per year compounded weekly. Determine the total interest Mike earned after 3 years.
3. Jeremy plans to go on a cruise 4 years from now. He will need $7500 at that time. What principal should Jeremy invest now at 8.4% per year compounded monthly to obtain the required amount?
4. Adrian wants to have $15000 in 3 years to start a mechanic shop. He plans to save the money by making regular deposits into an annuity that earns 4.8% compounded monthly. What monthly deposits does Adrian have to make?
1) :
a - [1 + 0.018/12]^12=1.018149 - 1 x 100 =1.815% compounded monthly.
b - [1 + 0.018/4]^4 =1.018122 -1 x 100 =1.8122% componded quarterly.
c - [1 + 0.018/52]^52=1.018160 - 1 x 100=1.816% compounded weekly.
d -[1 + 0.018/365]^365=1.0181625 - 1 x 100=1.81625% componded daily.
2):
FV = PV[1 + R]^N
FV =10,000 [1 + 0.06/52]^(3*52)
FV =10,000 x 1.19709313870..........
FV =$11,970.93 - The amount in Mike's account after 3 years.
$11,970.93 - $10,000 =$1,970.93 Total interest earned.
3):
PV = 7,500 / [1 + 0.084/12]^(4*12)
PV = 7,500/ [1.007]^48
PV = 7,500/ 1.39770199988.......
PV =$5,365.95 - This is what Jeremy must invest today.
4):
This is the formula you would use to calculate this one:
FV = PMT{[1 + 0.048/12]^(3*12) - 1 / (0.048/12)}
15,000 =PMT {[1.004]^36 -1 / (0.004)}
15,000 =PMT x 38.638108459.........
PMT = $15,000 / 38.638108459...........
PMT=$388.22 Monthly payment that Adrian must make every month for 3 years.
