Financial Calculations Exercises
1 .- Telefónica bought shares late last year to 15.85 euros. Today, two and a half months later, is trading at 14.14 euros. What is the compound annual percentage rate on my investment?
a) -10.79%
b) -2.35%
C) -42.19%
d) -51.79%
We just have to replace the formula under the composite type, expressing the time in years:
14.14 = 15.85 * (1 + i) ^ (2.5/12), and therefore po, i = (14.14/15.85) ^ (12/2.5) -1 =- 0.42188
2 .- A commercial paper maturing in 175 days, with a nominal value of 1500 euros, discounted at 3.5% applies today:
a) 1474.828767
B) 1474.479167
c) 1474.906111
d) 982.9861111
The discount on the commercial is simple Act/360. This discounted value = 1500 * (1-3.5% * 175/360) = 1474,479
3 .- We want to save a total of 150,000 euros in 10 years. To do this, we will provide a savings plan at 3% a fixed amount at the end of each year. This amount is
a) 12.703,47
b) 17.584,58
C) 13.084,58
d) 15.000,00
We apply the formula for the final value of a post-paid annual fee income: FV = PV * (1 + i) ^ n = share * (1 – (1 + i) ^ (-n)) / i * (1 + i ) ^ n. So share = FV / ((1 – (1 + i) ^ (-n)) / i * (1 + i) ^ n) = 150000 / ((1 – (1 +3 %)^(- 10) ) / 3% * (1 +3%) ^ 10) = 13084.58.
4 .- If we have an annual deposit that pays a 5% APR for 4 months, and then a 3% APR the rest of the time, providing we get 1200 euros at the end of the year:
A) 1243.948772
b) 1243.557201
c) 1244
d) 1251.948662
We must apply capitalization composed during two consecutive periods, equaling the value end of the first period with the middle initial: Cf = 1200 * (1 +5%) ^ (4 / 12) * (1 +3%) ^ (8 / 12) = 1243,949
5 .- We bought a car for 25,000 euros and agree to finance
5 years at 7% APR, with shares
monthly at the end of each month. The fees for this loan would be:
a) 6097.27
B) 492.50
c) 351.14
d) 497.74
First, we need to move to monthly rate APR. I (monthly) = (1 + APR) ^ (1 / 12) -1 = (1 +7%) ^ (1 / 12) -1 = 0.005654 = 0.5654%. It also may have reached this number by calculating the nominal rate (which gives 6.78497% divided by 12). Then apply the formula for PV of income postpaid to share respñver. PV = share * (1 – (1 + i) ^ (-n)) / i, so share = 25000 / ((1 – (1 +0.5654 %)^(- 60)) / 0.5654%) = 492.4956
6 .- We have a bonus of $ 100 principal and coupon of 5% to 4 years. If the current price is 102, what is the bond yield?
a) 5%
b) 4.6739%
c) Unable to calculate with the data provided
D) 4.4432%
The flow scheme to solve is -102, 5, 5, 5, 105 respectively. Also be resolved as capitalization compound, indicating FV = 100, PV =- 102, PMT = Payment = 5, n = 4. The result can only be given numerically, with calculator: 4.4432%.
7 .- An investment fund, in 2008, has had the following average returns: average monthly return (non-continuous) = 0.75% average monthly return continuous = 0.67%. If we invest 1500 euros in the fund earlier this year, we end
a) 1620.60
B) 1625.58
c) 1640.71
d) 1635
Only with the log-return (return continuous) media we can recover the final value. Thus, if the monthly average is 0.67%, the annual 12 * 0.67% = 8.04%,and the final value = 1500 * exp (0.0804) = 1625,581 8 .- If we contribute to a pension plan at the beginning of $ 10,000 each year for 20 years, what is the minimum annual return must have a plan to secure a final amount of 300,000 euros?
A) 4.07151%
b) 3.71888%
c) 3.91222%
d) gives a negative value
When asking about the type of profit or income, calculator needs to be addressed. In this case, FV = 300000, rent prepaid, PV = 0, share = PMT = payment = 10000, n = 20, which determines an i% = 4.0715%
9 .- A product for four years gives us 1000 euros, collecting 30, 40, 50 and 60 at the end of each of the four years. Similarly, in the end, returned euros from 1000. If interest rates are at 4%
A) invest in the product
b) not invest in the product
c) I can not give an answer with the data we have
d) I need the product in order coupon value goods
The product is going to pay 30, 40, 50 and 1060 euros each year. These amounts, discounted at 4% add 30 / (1 +4%) +40 / (1 +4%) ^ 2 +50 / (1 +4%) ^ 3 +1060 / (1 +4%) ^ 4 = 1016.371, as this is the maximum price I will be willing to pay. Since you ask 1000 euros, the priducto offers good conditions, and therefore a yield above 4% requirement.
10 .- Seek continuous annual rate equivalent to a compound monthly rate of 1%
A) 11.9404%
b) 11.3328%
c) 12.6825%
d) 0.99503%
A compound monthly rate of 1% spends 100 euros to 101 in 1 month. Substituting these data into the formula for continuous compounding, 101 = 100 * exp (I/12), so that i = 12 * ln (101/100) = 0.119404