# Thread: Annual Interest & Capital Equation

1. ## Annual Interest & Capital Equation

I have been studying for a mathematics entrance test and the following problem came up on the practice exam:

Capital K is deposited at an annual interest rate of 4%. Interest is compounded
once a year. In fifteen years time the capital has grown to an amount of
108056.62 euro. Compute the principal capital K.

Could anyone suggest a formula/formulas for solving this problem. Also, could anyone suggest an area of mathematics to concentrate my efforts toward problems such as the above.

Thank you,

Matty

2. Deposit: K
1 year later: K*(1.04)
2 years later: K*(1.04)*(1.04) = K*(1.04)^2
3 years later: K*(1.04)^3
...
15 years later: K*(1.04)^15 = 108,056.62

For me, the concept of "a formula" is very, very weak. Figure it out! Make your own formulae. The area of concentration you should pursue is in solving problems, rather than in memorizing things. Take a deep breath and think it through.

3. ## Formula

TK -

I understand the formula you wrote. However, I guess I went blank when you wrote (1.04) in the context of the formula. I thought it would be (0.04) which equals 4%. Is the (1.04) because the "1" is equal to 100% of K?

Thank you,

Matty

4. You have it.

.04 * K is the interest earned in the first year. You must then add that interest to the original amount, K, to manage the accumualted value one year after the deposit.

K + 0.04*K = 1.00*K+ 0.04*K = K*(1.00 + 0.04) = K*1.04

5. So given the formula K*(1.04)^15 = 108,056.62, K should = 60,000...?