Question

how do you arrive at this answer??

14-38 Your beginning salary is $68,000. You deposit 8% each year in a savings account that earns 3% interest. Your salary increases by 5% per year and inflation is 2.5% per year. What value does your savings account show after 30 years? What is the value in Year-1 dollars?

Answer 1

ANSWER:

Since the calculations are extremely long i have solved in excel.

year	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
salary increase each year at 5%		68000	71400	74970	78718.5	82654.425	86787.14625	91126.50356	95682.82874	100466.9702	105490.3187	110764.8346	116303.0764	122118.2302	128224.1417	134635.3488	141367.1162	148435.472	155857.2456	163650.1079	171832.6133	180424.2439	189445.4561	198917.729	208863.6154	219306.7962	230272.136	241785.7428	253875.0299	266568.7814	279897.2205
savings 8% of salary		5440	5712	5997.6	6297.48	6612.354	6942.9717	7290.120285	7654.626299	8037.357614	8439.225495	8861.18677	9304.246108	9769.458414	10257.93133	10770.8279	11309.3693	11874.83776	12468.57965	13092.00863	13746.60906	14433.93952	15155.63649	15913.41832	16709.08923	17544.54369	18421.77088	19342.85942	20310.00239	21325.50251	22391.77764
pv at 3% (using npv function) =npv(rate,savings from year 1 to year 30)	212318.59

Now we will the fv at 30 years.

1) fv = pv(f/p,i,n)

fv = 212,318.59(f/p,3%,30)

fv = 212,318.59 * 2.43

fv = $515,352.93 or $515,353

2) value in year 1 dollars:

n = 29 (30 - 1)

i = 2.5% (inflation)

pv = fv(p/f,i,n)

pv = 515,353(p/f,2.5%,29)

pv = 515,353 * 0.4886

pv = $251,826