Question

What​ payment, made at the end of each three months for 13 ​years, will accumulate to $ 11 comma 300 at 6 % compounded semi dash annually question mark

The required quarterly payment is ​$

nothing.

​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

Answer 1

Annual interest rate = 6.00%
Semiannual interest rate = 6.00% / 2
Semiannual interest rate = 3.00%

Effective annual rate = (1 + Semiannual interest rate)^2 - 1
Effective annual rate = (1 + 0.03)^2 - 1
Effective annual rate = 1.0609 - 1
Effective annual rate = 0.0609

Quarterly interest rate = (1 + Effective annual rate)^(1/4) - 1
Quarterly interest rate = (1 + 0.0609)^(1/4) - 1
Quarterly interest rate = 1.014889 - 1
Quarterly interest rate = 0.014889

Desired sum = $11,300
Time period = 13 years or 52 quarters

Let quarterly payment be $x

$x*1.014889^51 + $x*1.014889^50 + … + $x*1.014889 + $x = $11,300
$x * (1.014889^52 - 1) / 0.014889 = $11,300
$x * 77.679762 = $11,300
$x = $145.47

Quarterly deposit = $145.47