Submitted by Sydney Sales on Sat, 05/02/2020 - 12:58 pm.

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## New forum topics

- At 2:00 pm,thermometer reading 80oF.itis taken outside where the air temp is 20oF. At 2:03 pm, the temp reading yielded by the thermometer is 42oF. Later it was brought inside at 80oF. At 2:10 the reading is 71oF. When was the thermometer brought indoors?
- What 'positive' values of x, y, and z that will make x/(y+z) + y/(z+x) + z/(x+y) = 4?
- A man wishes his son to receive P200,000 ten years from now. What amount should he invest now if it will earn interest of 10% compounded annually during the first 5 years and 12% compounded quarterly during the next 5 years.
- Among 10000 random digits, find the probability that the 3 appears at most 950 times.
- Is this a rule in semi circles?

## Active forum topics

- At 2:00 pm,thermometer reading 80oF.itis taken outside where the air temp is 20oF. At 2:03 pm, the temp reading yielded by the thermometer is 42oF. Later it was brought inside at 80oF. At 2:10 the reading is 71oF. When was the thermometer brought indoors?
- Find the differential equation of family of circles with center on the line y= -x and passing through the origin.
- What 'positive' values of x, y, and z that will make x/(y+z) + y/(z+x) + z/(x+y) = 4?
- A man wishes his son to receive P200,000 ten years from now. What amount should he invest now if it will earn interest of 10% compounded annually during the first 5 years and 12% compounded quarterly during the next 5 years.
- Among 10000 random digits, find the probability that the 3 appears at most 950 times.

## Solution 1 $F = P(1 + i)^n$ …

## Solution 1

$F = P(1 + i)^n$

$F_5 = P(1 + 0.10)^5$

$F_5 = 1.10^5P$

$F_{10} = F_5(1 + 0.03)^{20}$

$F_{10} = 1.10^5P(1.03^{20})$

$F_{10} = (1.10^5)(1.03^{20})P$

$F_{10} = 20\,000$

$(1.10^5)(1.03^{20})P = 20\,000$

$P = \text{P}6,875.78$

answer## Solution 2

$P = \dfrac{F}{(1 + i)^n}$

$P_5 = \dfrac{20\,000}{(1 + 0.03)^{20}}$

$P_5 = \text{P}11,073.52$

$P_0 = \dfrac{P_5}{(1 + 0.10)^5}$

$P_0 = \dfrac{11,073.52}{1.10^5}$

$P_0 = \text{P}6,875.78$

$P = P_0$

$P = \text{P}6,875.78$

answer