Question

Your bank pays 4% annual interest compounded quarterly on January 1, April 1, July 1, and October 1. You deposited $840 on April 1 and made no other deposits or withdrawals. Find your savings account balance on January 1 of the next year.

and
Your bank pays 4% annual interest compounded quarterly on January 1, April 1, July 1, and October 1. You deposited $840 on April 1 and made no other deposits or withdrawals. How much interest did you earn for these nine months?

Answer 1

The interest earned in 9 months is $25.45284

Explanation:

The interest rate given by the bank = 4%

The rate at which the interest is applied = Quarterly

The amount of money deposited = $840

The formula for compound interest is given as follows;

`Compound \ interest = P * \left [ \left(1 + (r)/(n) \right )^(t * n) - 1\right ]`

Where;

P = The principal = $840

r = The rate = 4% = 0.04

n = The number of times the interest is compounded per period = quarterly = 4

t = The time duration in period = 9 months = 3/4 × 1 year

Substituting the values gives the Compound interest C.I. as follows;

`C.I. = 840 * \left [ \left(1 + (0.04)/(4) \right )^{(3)/(4) * 3} - 1\right ] = 840 * \left [ \left(1 + (0.04)/(4) \right )^( 3) - 1\right ] = \$ 25.45284`

The interest earned in 9 months = $25.45284.