Compounding interest problem?

Forget excel or other spreadsheet programs. this is basic math. let me demonstrate.

Just memorise the annuity formula, and the compound interest formula. 10 years with semi annual payments equate to 20 periods. Also, because this is semi-annual, halve the annual rate, 9.5%, to get the semi annual rate; this would be 4.75%.

1. the value of the investment after 10 years (20 periods) is equivalent to the following, the annuity formula:

X ( (1+r)^n -1 )/r

The latter part of the equation is the annuity factor.

we subsitute the values

310 ( (1 + 0.0475)^20 - 1)/0.0475

= $9,983.746698 (always retain accuracy in your workings until the very end)

So after 10 years the value of investment is $9,984 (approx).

2. Now the regular payments have stopped, and we just let the investment grow with interest. to calculate what the size of investment will be for the next 8 years, we use the interest growth formula

X (1+r)^n

The semi annual interest is simply derived by dividing the 9.5% by two, and remember that there are two intervals per year (semi-annual).

so this becomes:

9,983.746698 (1+0.0475)^16

= $20,977.70916

round this up to the nearest dollar, this becomes:

$20,978.

Although it is easier with Excel or a similar spreadsheet program, the method is the same

Payment #1 = 310

After payment #2 the new balance will be (310 X 1.0475) +310 = 634.72

After payment #3 the new balance will be (634.72 X 1.0475) +310 = 974.87

Repeat through payment #20, then repeat 16 more times without adding the 310

Edit: If you are doing it on a calculator, you can compress the last step down to multiplying the #20 result by 1.0475^16 (i.e. to the sixteenth power)

(just tried it on Excel and came out with 20,977.71)