Maths Assignment HELLLPPPPPPPPP!!!! Legend Needed

Okay, so what we're looking at here is exponentials and logarithms.

note; my first assumption is that Semiannual means "one half year" or "two times a year", so in question 1. we're really looking at 8*2 = 16 payouts.

For question 1 (as an example):
firstly, normalise the repay so you know how much (as a factor) you've gained:
\( {64010 \over 35000} = 1.82885714....\)

This makes our maths a lot easier.

Next thing we want to know, is what percentage increase (interest rate) do we want to compound every 6 months, so that after 8 years (or 16 iterations) we get to 1.82885714...

The "compound" part basically means that every time you gain interest, next time you'll be getting interest on your new balance:
5% interest, 3 years: 1 * 1.05 = 1.05 (one year) , 1.05 * 1.05 = 1.1025 (second year), 1.1025 * 1.05 = 1.157625 (third year) etc...

*Right, nearly at the end now!*

In the 5% interest example above, we knew what percentage we had, and how long we are compounding the interest for, and we found the result after 3 years.

However, for question 1, we don't know the interest, but we do know the end result = 1.82885714.

Your ultimate formula is

\(( 1 + interest ) ^ {iterations} =end value\)

converted to:

\({endvalue} ^ {1 \over {iterations} } = (1 + interest)\)

(I'm assuming you've met "powers" before, i.e. 2^2 = 4, 2 ^ 3 = 8, 3 ^ 5 = 243 etc).

so your interest for Q1 is:

\(1.828857^{1 \over 16} = 1.03845\)

interest = 3.845%

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thankyou your. the best. i actually calculated the answer on some random website and it took me a while but i got 7.69% as an interest rate but the thing is on the website it didn't have any working out or formula's it just gave me the answer. i klnew it was right. and i think all you needed to do was multiply your final answer by 2 and i got the answer. so i'm very much appreciative of your work. you've helped me so much. i hope good things come to you... again thankyou. your a legend

OK, young person. Here is the interest rate for your loan:

1) 7.69% compounded semi-annually. This is how you get that rate:

FV=PV [1 + R/2]^N, Where R=Interest rate per period, N=number of periods, PV=Present value, FV=Future value.

64,010=35,000[1 + R/2]^8*2 Divide both sides by 35,000,

1.828857..=[1 + R/2]^16 Take the log of both sides.

0.26218...=16 x log[1 + R/2]

log[1 + R/2] =.26218/16=..0.016386...

[1 + R/2] =10^0.016386=1.0384515

R/2=1.0384515 - 1 =0.0384515

R=2 x 0.0384515

R=0.0769 x 100

R=7.69% compounded semi-annually.

PS. All the rest are calculated the same way. Good luck to you.

2) Interest rate =3.86% compounded Bi-weekly or every 2 weeks for 1/2 a year.

3) Interest rate=7.75% compounded annually over a period of 9 years.

4) Interest rate=7.66% compounded monthly over a period of 1.5 years.

Thankyou so much. you're a legend too if you're a different person to the first one. thankyou so so much guys. you's have been a huge help