Question

sabrina deposits $300 inta an savings at the end of each month for 5 years. if accumulated value of the deoposit is $20000 and interest is compounded semi-annually, calculate the nominal rate of interest

Answer 1

Future value = A/i*[(1+i)^n-1]

Future value = $20000

A = $300

n = 5*12 = 60

$20000 = $300/i * [(1 + i)^60 - 1]

Let i = 0.40%

$300/0.004[(1+0.004)^60-1]

$75000*[1.27064-1]

$75000*0.27064 = $20703

Let i = 0.30%

$300 / 0.003[(1+0.003)^60-1]

$100000[1.19689-1]

$100000*0.19689= $19689

As per interpolation method,

0.30% + ($19689 - $20000)/ ($19689 - $20703) *(0.40 - 0.30)

0.30% + (-$311 / -$1014)*0.10

0.30% + 0.0307%

0.3307%

One month interest rate = 0.3307%

Half yearly interest rate = (1 + 0.003307)^6 - 1 = 1.02 - 1 = 0.02 i.e. 2%

Nominal rate of interest = 2%*2 = 4% compounded semi annually