Intertemporal Open Market Macro question- Foreign country lending to Domestic country

> Consider two countries - a domestic country (with excess capacity and
> unlimited supply of labour) and a benevolent foreign country. The
> domestic country produces a single good at a fixed price of **Rupee**
> $ 1$ per unit and is in equilibrium initially (i.e., in year $0$) with
> income at Rs. 100 and consumption, investment and savings at **Rs.**$
> 50$ each. Investment expenditure is autonomous. Final expenditure in
> any **year** $t$ shows up as income in **year t** (say, **Yt**) , but
> consumption expenditure in **year t** (say, **Ct**) is given by:
> $C_{t} = 0.5Y_{t-1}$. The foreign country agrees to give a loan of
> **Rs.100** to the domestic country in **year 1** at zero interest rate, but on conditions that it be
> ***(i) used for investment only and (ii) repaid in full at the beginning of the next year***. The loan may be renewed every year, but
> on the same conditions as above. Find the income, consumption,
> investment and savings of the domestic country in **year 1, year 2**
> and in final equilibrium when the country takes the loan in **year 1**
> only.

Hello, there has been a lot of confusion regarding the correct solution to this question.

Some of the possible solutions are listed below:


>**(1)** As in year $0$ we are starting with $Yo=100$ so at the beginning of
> $year 1$ $C_{1}=0.5*100=50$
>
> $S_{1}=50 (Yo-C1)$
>
> now loan has also been taken this year so $I=100 + 50 (50=savings)$.
>
> The economy at the end of $year 1$, $Y_{1} = 150+50=200$
>
> now for $year 2$
>
> loan has to be repaid i.e $200-100$.
>
> $100$ remains in the economy $C_{2}=0.5*y_{1}=0.5*200 = 100$
>
> since there was $100$ in the economy and all is consumed so $S_{2}=0$
>
> loan has been taken this year also so $I=100+0 (0 is savings)$
> economy at the end of $year 2$ ,$y_{2}=100+100=200$
>
> this goes on for subsequent years in which saving always remains $0$.

and this is another possibility:


> **(2)** Period $1$: $Y=C+I+Loan taken$ : $200=50+50+100$
>
> Period $2$: $C=0.5*200= 100$ Autonomous investment= $50$
>
> Y should be $100+50=150$
>
> But repayment of loan: So $Y =150-100=50$
>
> Therefore: $50= 100+50 -(100)$
>
> Therefor savings= $(-100)$
> **No equilibrium**

**Any help as to what is the right approach to this problem will be appreciated!**