Question

Present and future value tables of $1 at 3% are presented below:

N FV $1 PV $1 FVA $1 PVA $1 FVAD $1 PVAD $1
1 1.03000 0.97087 1.0000 0.97087 1.0300 1.00000
2 1.06090 0.94260 2.0300 1.91347 2.0909 1.97087
3 1.09273 0.91514 3.0909 2.82861 3.1836 2.91347
4 1.12551 0.88849 4.1836 3.71710 4.3091 3.82861
5 1.15927 0.86261 5.3091 4.57971 5.4684 4.71710
6 1.19405 0.83748 6.4684 5.41719 6.6625 5.57971
7 1.22987 0.81309 7.6625 6.23028 7.8923 6.41719
8 1.26677 0.78941 8.8923 7.01969 9.1591 7.23028
9 1.30477 0.76642 10.1591 7.78611 10.4639 8.01969
10 1.34392 0.74409 11.4639 8.53020 11.8078 8.78611
11 1.38423 0.72242 12.8078 9.25262 13.1920 9.53020
12 1.42576 0.70138 14.1920 9.95400 14.6178 10.25262
13 1.46853 0.68095 15.6178 10.63496 16.0863 10.95400
14 1.51259 0.66112 17.0863 11.29607 17.5989 11.63496
15 1.55797 0.64186 18.5989 11.93794 19.1569 12.29607
16 1.60471 0.62317 20.1569 12.56110 20.7616 12.93794

You want to invest $20,000 today to accumulate $22,500 to buy a car. If you can invest at an interest rate of 3% compounded annually, how many years will it take to accumulate the required amount?

Answer 1

To accumulate $22,500 from a $20,000 investment at a 3% annual interest rate, it would take approximately 4 years, based on the future value formula and logarithmic calculations.

Step-by-step explanation:

To determine how many years it will take to accumulate $22,500 at an annual interest rate of 3%, you use the future value formula, which is:

Future Value = Principal × (1 + interest rate)time

We know the Future Value ($22,500), the Principal ($20,000), and the interest rate (3% or 0.03). We need to find the time (number of years). We can rearrange the formula to solve for time:

time = log(Future Value / Principal) / log(1 + interest rate)

Substituting the given values:

time = log($22,500 / $20,000) / log(1 + 0.03)

time = log(1.125) / log(1.03)

time ≈ 3.89

The closest whole number of years would be 4 years, since you cannot accumulate fractional parts of a year. Therefore, it will take approximately 4 years to accumulate the required amount of $22,500 using a 3% interest rate compounded annually.

Answer 2

binder: Liquid substance used in paint and other media to bind particles of pigment together.

fresco: Where pigments are mixed with water and then applied to a plaster support, usually a wall or a ceiling.

gouache: A type of watercolor in which white pigment is added creating a duller effect, and a tinted feel.

oil: Painting medium where pigments are binded using oils, usually linseed oil.

painting media: Material made of three components; pigment,vehicle, and binder

pigment: Ground up solids that contain color the color in paint.

tempera: A water based painting medium made with egg yolk, often used to paint frescos and panels.

vehicle: Adjusts the viscosity of the paint.

watercolor: Pigment that is mixed with arabic and gum, and mostly water before it is applied to the paper.

Painting Media

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Step-by-step explanation: