Question

Present Value of $1 at 5% for 5 periods .78353 Present Value of $1 at 6% for 5 periods .74726 Present value of $1 at 10% for 5 periods .62092 Present Value of $1 at 12% for 5 periods .56743 Present Value of $1 at 5% for 10 periods .61391 Present Value of $1 at 6% for 10 periods .55840 Present value of $1 at 10% for 10 periods .38554 Present Value of $1 at 12% for 10 periods .32197 Present Value of Ordinary Annuity at 5% for 5 periods 4.32948 Present Value of Ordinary Annuity at 6% for 5 periods 4.21236 Present value of Ordinary Annuity at 10% for 5 periods 3.79079 Present Value of Ordinary Annuity at 12% for 5 periods 3.60478 Present Value of Ordinary Annuity at 5% for 10 periods 7.72174 Present Value of Ordinary Annuity at 6% for 10 periods 7.18883 Present value of Ordinary Annuity at 10% for 10 periods 6.14457 Present Value of Ordinary Annuity at 12% for 10 periods 5.65022 Future Value of $1 at 5% for 5 periods 1.27628 Future Value of $1 at 6% for 5 periods 1.33823 Future value of $1 at 10% for 5 periods 1.61051 Future Value of $1 at 12% for 5 periods 1.76234 Future Value of $1 at 5% for 10 periods 1.62889 Future Value of $1 at 6% for 10 periods 1.79085 Future value of $1 at 10% for 10 periods 2.59374 Future Value of $1 at 12% for 10 periods 3.10585 Future Value of Ordinary Annuity at 5% for 5 periods 5.52563 Future Value of Ordinary Annuity at 6% for 5 periods 5.63709 Future value of Ordinary Annuity at 10% for 5 periods 6.10510 Future Value of Ordinary Annuity at 12% for 5 periods 6.35285 Future Value of Ordinary Annuity at 5% for 10 periods 12.57789 Future Value of Ordinary Annuity at 6% for 10 periods 13.18079 Future value of Ordinary Annuity at 10% for 10 periods 15.93743 Future Value of Ordinary Annuity at 12% for 10 periods 17.54874 On January 1, 2019, Carly Company decided to begin accumulating a fund to replace equipment in five years. The company plans to make semiannual deposits of $30,000 during five years at June 30 and December 31 each year. The first deposit was made at June 30, 2019. What will be the balance of the fund in five years at a 10% interest rate? Please use the following format for your answer $XX,XXX,XXX.XX

Answer 1

In the given case,Carly Company decided to begin accumulating a fund to replace equipment in 5 years by making semiannual deposits of $30,000 during five years at June 30 and December 31 each year bearing 10% interest. The first deposit was made at June 30, 2019.Therefore the number of installments will be over 10 periods on the following dates-30.06.2019,31.12.2019,30.06.2020,31.12.2020,30.06.2021,31.12.2021,30.06.2022,31.12.2022,30.06.2023 and 31.12.2023.

When recurring payments of the same amount is made using the same interest rate over a period of time maturing at a particular date,the maturity value is calculated using the future value of an ordinary annuity.

Therefore the balance of the fund at the end of 5 years shall be calulated by multiplying the installment amount with the future value of ordinary annuity @5% for 10 periods.Rate considered as 5% as 10% is the yearly rate and each year has 2 periods hence rate per period will be 5%.

Hence the value of fund is $30,000*12.57789=$377,366.70