Maths Question?

Can anyone show me how you work this out.

person A has 锟?00 in the bank

person B has 锟?80 in his hand

With the interest rate @ 5% how many years will it be before person A has more than person B?

whats the equation for working this out?

thanks

Maths Question?tax credit

1.05^n = 1.8

take logs of both sides and rearrange

n = log(1.8)/log(1.05) = 12.0472 years

To do it iteratively (the lazy way)

100 * 1.05 (add 5%) = 105

105 * 1.05 (add another 5%) = 110.25

110.25 * 1.05 = etc etc etc

Maths Question?

loan

work out 5% of each one, SAY one is 锟?.54 keep adding it on SAY the other has 锟?.00 keep adding it until a has more than b|||The formula for compounding interest is:

FV = P(1+r)^n

where FV = future value, P = starting value (principal), r = rate of return, and n = units of time interest is accrued

So we want to know how many years it will be before the FV of 100 at 5%/year will be more than 180.

180 = 100(1 + 0.05)^n

180 = 100(1.05)^n

1.05^n = 1.8

Solve for n (hint, use logarithms) and you will have the number of years for them to be equal... after this time, A would have more than B.

I hope this helps! :) Best of luck.|||Surely if they are being paid interest at the same rate then a will never have more than b because b will be paid more interest.|||Hi

I will have a guess at 12years and 173 days|||There are TWO answers to this question. This is because A could be earning simple interest on his 锟?00 or he could be earning compund interest.

With simple interest A earns 5% of 锟?00 every year. The interest is not added to the original 锟?00. So at the end of year 1 he earns 锟?, at the end of year 2 another 锟? etc. So, every year he earns just 锟? on his 锟?00 saved. We will assume that he saves each of these 锟? but they don%26#039;t earn interest. At the end of year 16 he will have earned 锟?0 ansd thus have the same amount as B. At the end of year 17 he will have earned 锟?5 and will then have MORE than B.

With compound interest the interest earned at the end of each year is added to the original 锟?00. So at the end of year 1 A earns 5% of 锟?00, that is 锟?. At the end of year 2 he now earns 5% of 锟?05, that is 锟?.25. At the end of year 3 A earns 5% of 锟?10.25, that is 锟?.5125. This is the long method of calculating compound interest.

You can see that this is a pretty laborious way of calculating compound interest, so banks etc use a formula to calculate it. This is:

Total amount = P x (1 + R/100)^t

where:

P is the orginal amount invested called the PRINCIPAL

R is the percentage rate of interest

t is the time in years over which is being calculated

So you have:

Total amount = 100 x (1 +5/100)^t

You want to know t when the total amount is %26gt; 锟?80. Thus you need to solve:

100 x (1 + 5/100)^t %26gt; 180

100(1.05)^t %26gt; 180

1.05^t %26gt; 180/100

1.05^t %26gt; 1.8

Take the log of both sides:

log1.05^t = log 1.8

t log1.05 %26gt; log 1.8

t %26gt; log 1.8/log 1.05

t %26gt; 12.047

So A will have %26gt; 锟?80 after 12.047 years. Note, however, that this means in practice A will have more than 锟?80 after 13 years because interest is only paid at the end of the year.

Also, these calculations ignore any tax that has to be paid.