SOLUTION: A debt of x pesos, with interest rate of 7% compounded annually will be retired at the end of 10 years through the accumulation of deposit in the sinking fund invested at 6% compou

Question 1118883: A debt of x pesos, with interest rate of 7% compounded annually will be retired at the end of 10 years through the accumulation of deposit in the sinking fund invested at 6% compounded semi-annually. The deposit in the sinking fund every end of six months is P21,962.68. What is the value of x?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the debt is x pesos.
the interest rate is 7% compounded annually for 10 years.

the deposit in the sinking fund is 21,962.68 at the end of every 6 months at 6% interest per year compounded semi-annually.

the interest rate of 6% per year divided by 2 equal an interest rate of 6% every semi-annual period.

use a financial calculator to find the future value of this investment.

the future value of the investment at the end of 10 years is 590,145.4364.

take the present value of this amount for 10 years at 7% compounded annually.

you will get a present value of 300,000.0148 pesos.

that's the value of x which is the original debt.

the online financial calculator you can use is at https://arachnoid.com/finance/

here are the results of finding the future value of the payments at the end of every 6 months.

interest rate was 3% every semi-annual period of 6 months.
number of time periods is 10 years * 2 semi-annual periods per year = 20 semi-annual periods.

$$$

here are the results of finding the present value of that amount for 10 years.

interest rate was 7% every annual time period.
number of time periods is 10 years * 1 = 10 annual time periods.

$$$

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