Question

A bank pays 8% annual interest, compounded daily, on savings deposits. Find the value after five years of $500 deposit in this account

Answer 1

The value of money after 5 years is $ 745.77

Solution:

The formula for total amount in compound interest is given as:

`A = p(1+(r)/(n))^(nt)`

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

Here given that,

P = 500

t = 5 years

n = 365 ( since interest is compounded daily)

`r = 8 \5 = (8)/(100) = 0.08`

Substituting the values we get,

`A = 500(1+(0.08)/(365))^(365 * 5)\\\\A = 500(1+0.0002191)^(1825)\\\\\text{Simplify the above expression }\\\\A = 500(1.0002191)^(1825)\\\\A = 500 * 1.491546\\\\A = 745.77`

Thus the value of money after 5 years is $ 745.77