A bank has launched a three year structured deposit that offers an effective rate of interest of $8$% perannumfor the first $18$ months, $1.5$% per quarter for the next 6 months and $2$% per half year for the last 12months. If I wish to accumulate $100,000$ on the maturity date how much should I invest?
$100,000=X[(1.08)^{1.5}+(1.08)^{1.5}(1.00375)^2+(1.08)^{1.5}(1.00375)^2(1.01)^2]$
Solving for $X$ does not give the answer.
FV of the investment X at the end of 18 months:
$$FV_{18}= X(1.08)^{1.5}$$
This becomes the present value for the next period with different interest rate and for the next 6 months
$$FV_{24} = (X(1.08)^{1.5})\times(1.015)^2$$
$$FV_{36} = ((X(1.08)^{1.5})\times(1.015)^2)\times (1.02)^2$$
Thus $FV_{36} = 100,000$, Then find $X = 83,125$