Question

Suppose, instead, Justin deposits 100 into a savings account, paying nominal interest rate i (2) = 2%, at the beginning of each half year for 10 years. The interest earned from this account can be withdrawn at the end of each year and reinvested into another account earning AEIR 4%. Find the accumulated value of his holdings (in both accounts) at the end of 10 years.

Answer 1

Calculation of accumulated value in both accounts:

In Account having interest rate of 2%, interest is withdrawn every year hence at the end of 10 years balance will be 100.
Now we have to calculate the interest earned every year in savings account which will become annuity for another account having Interest rate of 4%.

Annual Interest earned on savings account = [100 * (1 + 0.01)^2 ] - 100 = 2.01
Now we use the future value annuity formula for calculation of future value at the end of 10 years.
Future value of annuity = P * [((1+r)^n - 1) / r]
Here P = Annuity amount = 2.01
r = 4% or 0.04
n = no. of years = 10

Future value of annuity = P * [((1+r)^n - 1) / r]
= 2.01 * [((1+0.04)^10 - 1) / 0.04]
= 2.01 * 12.0061
= 24.13

Total accumulated value in both accounts = 24.13 + 100 = 124.13