Compound Interest Formulas For Financial Problems

The loan amount provided by the angel investor could be calculated as the present value of the amount paid after two years of time. The interest rate applicable for the transaction was around 6% payable semi-annually over the two-year time. The savings of $80,654 will be pulled back two years back at the semiannual rate of 6% payable semiannually (Eisenberg & Mishura, 2018).

Future Value = 80,654

Interest Rate = 6% payable semiannually.

Time= 2years

Calculated Present Value = 71,660.34

Int Rate Compounded Monthly
Future Value	80654
Time (In Years)	12
Interest Rate	5.93%
Int Rate Comp. Semi-Annually	0.004938
Factor	1.004938
Semi Annual Rate	1.060886
Present Value	71661.95

It would take around 71 month of time for the repayment and for reaching the debt of $100,000 assuming the interest rate of around 6% payable semiannually. The Present Value considered for the calculation was around 71,660 and the N (Time period was calculated using the back calculation for solving the same).

Future Value	80654
Time (In Years)	1.5
Interest Rate	8%
Int Rate Comp. Semi-Annually	0.0410067
Factor	1.0410067
Semi Annual Rate	1.062
Present Value (Value of the Loan)	71660.03

Future Value	80654
Time (In Years)	2
Interest Rate	6%
Int Rate Comp. Annually	6%
Factor	1.06
Semi Annual Rate	1.1236
Present Value (Value of the Loan)	63885.522

If the contract was for two years of time and the loan had to be settled in the same amount of time then the following amount 25,000 and 40,000. It would be repaid at the respective year end would be discounted at the todays rate at the all in interest rate of 6% to determine the fair value of the loan amount that can be granted. The final amount calculated for the loan amount was around $59,184.76 as the total amount (Xiong et al. 2016). 

The final amount of $80,654 will be pulled back at the respective mentioned period of two years with the rate of 6% compounded semiannually and 8% compounded quarterly. The rate calculated for the first year was 6.09% and the return for the second year was calculated to be around 8.24% that was the return calculated on a quarterly compounded basis.

The amount for the second year will be calculated as = (80,654/ (1.0824)) = 74,514.

The amount derived for the second year will then be pulled back for the first year as = (74514/1.0609) = 70,236.63

The size of the loan will be around 70,236.63 for the same to be repaid within the two year of frame time. 

References

Eisenberg, J., & Mishura, Y. (2018). An Exponential Cox-Ingersoll-Ross Process as Discounting Factor. arXiv preprint arXiv:1808.10355.

Xiong, J., Zhang, Q., Sun, G., Zhu, X., Liu, M., & Li, Z. (2016). An information fusion fault diagnosis method based on dimensionless indicators with static discounting factor and KNN. IEEE Sensors Journal, 16(7), 2060-2069.