The compound interest formula for money deposited in a bank

The compound interest formula for money deposited in a bank is given by A = P(l+i)^n. In our formula, i is the decimal giving the rate of interest each time the bank pays you interest, n is the number of times the bank pays you interest, P is the amount you originally deposited, and A is the amount in your account Most banks now pay interest monthly, though the rate posted is usually the annual rate. So suppose a bank posts that its annual interest rate is 3%. Write this as a decimal, and use it to write your monthly rate/as a decimal. (Divide yearly rate by 12.) Suppose you leave your money in the bank for 2 years and 6 months, before withdrawing it If the bank pays interest monthly, find n, the number of times the bank will pay you interest Now suppose you were given a $1000 bonus at work, and left it in the bank under the terms given in (ii) and (iii). Use the formula above to find the amount of money you will have when you withdraw. How much interest did the bank pay you in situation (iii)? Using the formula and results so far to answer this: Suppose that on January 1, 2019, you will need $10,000 to repay your gambling debts. How much money must you put in the bank this coming July 1, in order to repay your debts? Write in a clear English essay the results you have found in (i) through(v).

Solution

A = P( 1+i)^n

i) interest rate = 3%

i = 3/100 = 0.03

monthly rate i = 0.03/12 =0.0025

ii) time = 2year +6 months = 2+ 6/12 = 2.5 yrs

for monthly interests n = 2.5 *12 = 30

iii) Amount = $1000( 1+0.0025)^30 = $1077.78

iv) Interest = Amount - Principal = 1077.78 -1000 = $77.78

v) n = 30 months from 1st July 2016 to 1 jan2019

i = 0.0025

$10000 = Principal*1.07778

Principal = $9278.33 should be deposited on 1 July 2016