Number Pattern question (show step, thanks)?

Question

Suppose that $3000 is invested at6.5% annual interest, compound monthly.
a. What is the blance after 6 years?
b. Suppose $150 is added to the account every month. What is the balance after 6 years?

Answer 1

Create a Spreadsheet.

Column A, label 'month' (cell A1), and cells A2-A73 with the numbers 1 to 72 (i.e. 6 x 12 months)

In cell B1, put 3000

In B2 put formula = B1 * (1 + 0.065)

Now 'copy' and 'paste' the formula from B2 into cells B3 to B73

Answer (a) will be found in cell B73


Go back to cell B2.

Change the formula to = B1 * (1 + 0.065) + 150
(assuming the 150 is added at the end of the month)

Answer (b) is now in cell B73.

Answer 2

a. You are looking for the future amount of the investment whose present value is $3,000. The formula is P (1+i)^n where P is the principal, i is the interest rate, and n is the number of periods.

P (1 + .5416667)^72

Since compounding is monthly you have to use the monthly interest rate and n is the number of months in 6 years. The solution is $4,426.28

b. This is an annuity of $150 per month for 72 months. You want the future value of the annuity The formula is

R x ((1+i)^n-1)/i

where R is the monthly payment, called Rent, of $150

The solution to the annuity is $13,165.68

Combining the two amounts you get $17,591.96

It is simpler to use a financial calculator than to use the formulas. You can also find the answer by using spreadsheet functions for the time value of money.