Final answer:
The total amount after 5 years with an initial deposit of Php1,000 at a 10% per annum interest rate is Php1,610.51, following the compound interest formula A = P(1 + r/n)^(nt).
Step-by-step explanation:
To find the total amount of an initial bank deposit of Php1,000 after 5 years at an interest rate of 10% per annum compounded annually, we use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial deposit or loan amount).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
To solve for A, we substitute the given values into the formula:
A = 1000 (1 + 0.10/1)^(1*5)
A = 1000 (1 + 0.10)^5
A = 1000 (1.10)^5
A = 1000 * 1.61051
A = 1610.51
The total amount after 5 years is Php1,610.51, which corresponds to option b) Php1,610.51.