Question

Suppose a​ 40-year-old person deposits ​$12 comma 00012,000 per year in an Individual Retirement Account until age 65. Find the total in the account with the following assumption of an interest rate.​ (Assume quarterly​ compounding, with payments of ​$3 comma 0003,000 made at the end of each quarter​ period.) Find the total amount of interest earned. 55​%

Answer 1

Answer:  interest earned = $8942372340

$8942672340 this is amount after 25 years.

Explanation:

formula used:    S= R*[ (1+i )ⁿ-1 / i ]

where:

S is future value

R is periodic payment

i is interest rate period

n is number of periods

R= $3000

n= 65-40=25   now 25*4=100   QUARTERLY that is why we used 4

i = 55% which is equal to 0.55

so, for quarterly i= 0.55/4= 0.138

now putting them in formula given above

S= 3000*[ (1+0.138)¹⁰⁰-1] / 0.138

S= $8942672340 (future value )

total money deposited = number of period * periodic amount

                                        = $3000*100 = $300,000

interest earned = future value - total money deposited

                           = 8942672340 - 300,000

 interest earned = $8942372340