Question

In: Finance

If a merchant deposits $ 1500 annually at the end of each fiscal year into a...

If a merchant deposits $ 1500 annually at the end of each fiscal year into a retirement account that pays interest at the rate of 8% per year compounded annually, how much money will he have in his account at the end of 25 years?

Solutions

Expert Solution

$ 1500 is deposited each year at the end of the year.

Interest received each year = 8 %

As the new deposit is made at the end of the year, interest will be received at 8 % on the accumulated deposit of last year (on current year deposit, interest will not be given)

No. of years = 25 years.

The deposits are shown in the table below-

On 1st year deposit, no interest will be given as the deposit is made at the end of the year.

Each year total deposit will be calculated by adding deposits of previous year + deposit in current year + interest received in current year.

Interest will be provided on the amount of last year total deposit. Current year deposit will not be taken.

For example-

In 2nd year, interest will be calculated at 8 % on last year total deposit i.e 1500

= 8 % of 1500 = 120 $

In 2nd year total deposit will become = total deposit accumulated from last year + deposit this year + interest received

= 1500 + 1500 + 120 = 3120 $

In 3rd year,

Interest will be received at 8 % on 3120 $ = 249.6 $

Total deposit at end of 3rd year = 3,120 + 1500 + 249.6 = 4869.6 $

Likewise, it is calculatd for all years and it is shown in below table-

Year Deposited at end of each year ($) Interest Received in current year $ @ 8 % on deposit accumulated from last years   Total Deposit (in $)
= total deposit accumulated from last year + deposit this year + interest received
1 1,500 0 1500
2 1,500 120 3120
3 1,500 249.6 4869.6
4 1,500 389.568 6759.168
5 1,500 540.73344 8799.90144
6 1,500 703.9921152 11003.89356
7 1,500 880.3114844 13384.20504
8 1,500 1070.736403 15954.94144
9 1,500 1276.395315 18731.33676
10 1,500 1498.506941 21729.8437
11 1,500 1738.387496 24968.23119
12 1,500 1997.458496 28465.68969
13 1,500 2277.255175 32242.94487
14 1,500 2579.435589 36322.38045
15 1,500 2905.790436 40728.17089
16 1,500 3258.253671 45486.42456
17 1,500 3638.913965 50625.33853
18 1,500 4050.027082 56175.36561
19 1,500 4494.029249 62169.39486
20 1,500 4973.551589 68642.94645
21 1,500 5491.435716 75634.38216
22 1,500 6050.750573 83185.13274
23 1,500 6654.810619 91339.94335
24 1,500 7307.195468 100147.1388
25 1,500 8011.771106 109658.9099

Total amount accumulated at end of 25 years in account = 1,09,658.9099 $ (approx)

Hope it helps!


Related Solutions

If a merchant deposits $ 1500 annually at the end of each fiscal year into a...
If a merchant deposits $ 1500 annually at the end of each fiscal year into a retirement account that pays interest at a rate of 8% per year compounded annually, how much money will he have in his account at the end of 25 years?
A woman deposits ​$14,000 at the end of each year for 10 yearsin an investment...
A woman deposits $14,000 at the end of each year for 10 years in an investment account with a guaranteed interest rate of 4% compounded annually. (a) Find the value in the account at the end of the 10 years. (b) Her sister works for an investment firm that pays 3% compounded annually. If the woman deposits money with this firm instead of the one in part (a), how much will she have in her account at the end of 10 years? (c)...
You will make deposits of $1,000 at the end of each year for 40 years in...
You will make deposits of $1,000 at the end of each year for 40 years in your investment account. After the 40th deposit, you will immediately withdraw all money from the account to buy a retirement annuity for 35 years with equal annual payments (paid at year-end) from a life insurance company. If the annual rate of return over the entire period (75 years) is 5%, how much is the annual payment from the insurance company? The amount of your...
If a business manager deposits $60,000 in a bond fund at the end of each year...
If a business manager deposits $60,000 in a bond fund at the end of each year for twenty years, what will be the value of her investment: a. At a compounded rate of 6 percent? b. At a compounded rate of 4 percent? What would the outcome be in each case if the deposits were made at the beginning of each year?
You plan to make 15 deposits at the end of each year in an account that...
You plan to make 15 deposits at the end of each year in an account that pays 6% compound interest annually. If the first deposit is $ 1,000 and subsequently 500 are added each year to the amount deposited the previous year (1000, 1500, ...), the amount of the account at the end of the 15 years will be close to: a. $71,550 b. $97,777 c. $92,242 d. $87,021 e.No correct answer is provided.
A 2n-year annuity has deposits of X made at the end of each of the first...
A 2n-year annuity has deposits of X made at the end of each of the first n years and deposits of 2X made at the end of each of the next n years. The accumulated value of this annuity at the end of 2n years is 6000. Suppose that the annual effective rate of interest is i, where i > 0. You are given X i = 1500. Find the present value of this annuity at time t = 0.
Jake deposits 5000 at the end of each year in an investment fund earning an annual...
Jake deposits 5000 at the end of each year in an investment fund earning an annual effective interest rate of 11.6%. The interest from this investment fund is paid at the end of each year into a savings account which earns an annual effective interest rate of 2.1%. Find Jake's combined total accumulated value at the end of 16 years.
Jake deposits 5000 at the end of each year in an investment fund earning an annual...
Jake deposits 5000 at the end of each year in an investment fund earning an annual effective interest rate of 11.6%. The interest from this investment fund is paid at the end of each year into a savings account which earns an annual effective interest rate of 2.1%. Find Jake's combined total accumulated value at the end of 16 years.
Schneider Company has a May 31 fiscal year end and adjusts accounts annually. Selected transactions in...
Schneider Company has a May 31 fiscal year end and adjusts accounts annually. Selected transactions in the year included the following: Jan. 2 Sold $20,400 of merchandise to Sapounas Company, terms n/30. The cost of the goods sold was $12,240. Schneider uses the perpetual inventory system. Feb. 1 Accepted a $20,400, five-month, 5% promissory note from Sapounas Company for the balance due. (See January 2 transaction.) Interest is payable at maturity. 15 Sold $14,400 of merchandise costing $8,640 to Garrison...
Schneider Company has a May 31 fiscal year end and adjusts accounts annually. Selected transactions in...
Schneider Company has a May 31 fiscal year end and adjusts accounts annually. Selected transactions in the year included the following: Jan. 2 Sold $20,400 of merchandise to Sapounas Company, terms n/30. The cost of the goods sold was $12,240. Schneider uses the perpetual inventory system. Feb. 1 Accepted a $20,400, five-month, 5% promissory note from Sapounas Company for the balance due. (See January 2 transaction.) Interest is payable at maturity. 15 Sold $14,400 of merchandise costing $8,640 to Garrison...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT