Per capita real GDP in country L is three times as high as in country M. The economic growth rate in country M?

Question

Per capita real GDP in country L is three times as high as in country M. The economic growth rate in country M is 8 percent while country L’s economy grows at a rate of 5 percent.

Use table below to determine approximately how many years will it be before per capita GDP in country M surpasses per capita real GDP in country L.

Interest Rate
Number
of Years 3% 4% 5% 6% 8% 10% 20%
1 1.03 1.04 1.05 1.06 1.08 1.10 1.20
2 1.06 1.08 1.10 1.12 1.17 1.21 1.44
3 1.09 1.12 1.16 1.19 1.26 1.33 1.73
4 1.13 1.17 1.22 1.26 1.36 1.46 2.07
5 1.16 1.22 1.28 1.34 1.47 1.61 2.49
6 1.19 1.27 1.34 1.41 1.59 1.77 2.99
7 1.23 1.32 1.41 1.50 1.71 1.94 3.58
8 1.27 1.37 1.48 1.59 1.85 2.14 4.30
9 1.30 1.42 1.55 1.68 2.00 2.35 5.16
10 1.34 1.48 1.63 1.79 2.16 2.59 6.19
20 1.81 2.19 2.65 3.20 4.66 6.72 38.30
30 2.43 3.24 4.32 5.74 10.00 17.40 237.00
40 3.26 4.80 7.04 10.30 21.70 45.30 1470.00
50 4.38 7.11 11.50 18.40 46.90 117.00 9100.00

simplicitus · Accepted Answer

This is a simple algebra question. If you have to ask it, why in the Economics section and not in Math section of Yahoo Answers?

Let X be the per capita GDP of country L and let this be year 0. Then:

X(n) = X(0) (1 + 0.05)^n

Let Y be the per capita GDP of country M, then

Y(n) = Y(0) (1.0.08)^n

You are given that X(0) = 3 * Y(0) and are asked to find n such that X(n) = Y(n)

So you know:

3 * Y(0) (1 + 0.05)^n = Y(0) (1 + 0.08)^n

Divide both sides by Y(0) and you have a simple equation in one unknown: n.

3 * (1 + 0.05)^n = (1 + 0.08)^n

or

3 = [(1 + 0.08) / (1 + 0.05)]^n

I'd ignore the table, compute R = (1 + 0.08) / (1 + 0.05) on a calculator and get

3 = R^n or log 3 = n log R

log 3 and log R can be computed on a calculator and so you can divide to find n.

? · Answer

"The countries with the fastest rates of economic growth on the planet are Vietnam, followed by China. Both Communist countries. And the Chinese economy experianced an economic growth rate of 10% during the financial collapse" Thats because they have started to embrace capitalism. "whilst the US economy went backwards 2.4%" Thats because the US is embracing socialism. "And, When the Soviet Union was still functioning, from the period of 1928, the Soviet Union was experiacing economic growth rates twice as fast than the USA, and straight after the Communist Revolution it had a growth rate four times faster than the USA." Garbage. False numbers. The communist government fed those phony numbers to themselves and the world.

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Per capita real GDP in country L is three times as high as in country M. The economic growth rate in country M?

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