Compound Interest Question

Question

Hello, Can you help with explanation of this problem?

Art opened a savings account that earned compound interest, compounded monthly. After the initial deposit,

Art made no deposits and no withdrawals. At the end of 8 months his account balance was $499.54, and at the end

of 18 months the balance was $525.09. How much money did Art initially deposit in this account? Express

your answer to the nearest whole dollar.

Thanks in advance

Answer 1

499.54= P(1+r/12)^12(8/12)

= P(1+r/12)^8

525.09=P(1+r/12)^12(18/12)

= P(1+r/12)^18

525.09/499.54 = (1+r/12)^10

r/12 = -1 +(525.09/425.54)^(1/10)

r= -12+12(535.09/425.54)^(.1)

P= 525.09/(525.09/425.54)^.1

= original amount