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:

The interest earned in 9 months is $25.45284

Step-by-step 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;

[tex]Compound \ interest = P \times \left [ \left(1 + \dfrac{r}{n} \right )^{t \times n} - 1\right ][/tex]

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;

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

The interest earned in 9 months = $25.45284.

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