# math

posted by .

Suppose a young couple deposits \$700 at the end of each quarter in an account that earns 7.1%, compounded quarterly, for a period of 6 years. After the 6 years, they start a family and find they can contribute only \$200 per quarter. If they leave the money from the first 6 years in the account and continue to contribute \$200 at the end of each quarter for the next 18½ years, how much will they have in the account (to help with their child's college expenses)?

• math -

Part 1:
R=\$700 per quarter
i=7.1%/4 per quarter
n=6*4=24 quarters
S=future value
=R((1+i)^n-1)/i
=700((1+.071/4)^24-1)/(.071/4)
=\$20,720.40

After 6 years,
S1=future value (after 18.5 years) of initial investment
=S(1+i)^n
=\$20720.40(1+.071/4)^74
=\$76179.91

R=\$200 per quarter
i=7.1%/4 per quarter
n=18.5*4=74 quarters
S2=future value for further contributions
=200((1+.071/4)^74-1)/(.071/4)
=\$30,158.48

Total future value
= \$76179.91+\$30158.48
= \$106,338.39

## Similar Questions

1. ### finite math

A young executive deposits \$400 at the end of each month for 7 years and then increases the deposits. If the account earns 7.2%, compounded monthly, how much (to the nearest dollar) should each new deposit be in order to have a total …
2. ### math

A young executive deposits \$400 at the end of each month for 7 years and then increases the deposits. If the account earns 7.2%, compounded monthly, how much (to the nearest dollar) should each new deposit be in order to have a total …
3. ### Math

The winner of a popular lottery is offered one of two options: i) a lump sum of \$102 500 ii) \$1000 every month for 10 years If the money can be invested at 3.0% p/a, compounded monthly, which option should the winner choose?
4. ### Economics

Ben deposits \$5000 now into an account that earns 7.5 percent interest compounded annually. He then deposits \$1000 per year at the end of the first and second years. How much will the account contain 10 years after the initial deposit?
5. ### Finance

Bob Bryan made deposits of \$10,000 at the end of each quarter to Lion Bank, which pays 8% interest compounded quarterly. After 9 years, Bob made no more deposits. What will be the account's balance 4 years after the last deposit?

Susie has decided to make deposits at the end of each quarter in the amout of \$5,000. After three years, she makes more deposits and just lets the money sit there for two more years. What will be the balance in the account at the end …
7. ### Math

A person wants to establish an annuity for retirement purposes. He wants to make quarterly deposits for 20 years so that he can then make quarterly withdrawals of \$5,000 for 10 years. The annuity earns 7.32% interest compounded quarterly. …
8. ### Financial Math

A young executive deposits \$400 at the end of each month for 9 years and then increases the deposits. If the account earns 6%, compounded monthly, how much (to the nearest dollar) should each new deposit be in order to have a total …
9. ### Math

You plan to make 24 equal quarterly payments (payments are at the end of each period) into an account to pays 8% (per year compounded quarterly). If you need \$5,000 at the end of 10 years (i.e. 4 years after the last payment is made …
10. ### Math help

You plan to make 24 equal quarterly payments (payments are at the end of each period) into an account to pays 8% (per year compounded quarterly). If you need \$5,000 at the end of 10 years (i.e. 4 years after the last payment is made …

More Similar Questions