1) An $1,000 investment is made in a trust fund at an annual percentage rate of 12%, compounded monthly. How long will it take the investment to reach $2,000?

2) If a $100 deposit is made at a bank that pays 12% per year, compounded annually, determine how long it will take for the investment to reach $2000.

3) Kelly invests $5000 with a bank. The value of her investment can be determined using the formula Y=5000 (1.06) ^t, where y is the value of the investment at time t, in years. Approximately how many years will it take for Kelly's investment to reach $20,000?

4) $2000 is invested at 5% per year, compounded semi-annually. How long will it take for the investment to triple in value?

Question

Mathematics

Zaniyah Bailey

3 February, 14:36

1) An $1,000 investment is made in a trust fund at an annual percentage rate of 12%, compounded monthly. How long will it take the investment to reach $2,000?

2) If a $100 deposit is made at a bank that pays 12% per year, compounded annually, determine how long it will take for the investment to reach $2000.

3) Kelly invests $5000 with a bank. The value of her investment can be determined using the formula Y=5000 (1.06) ^t, where y is the value of the investment at time t, in years. Approximately how many years will it take for Kelly's investment to reach $20,000?

4) $2000 is invested at 5% per year, compounded semi-annually. How long will it take for the investment to triple in value?

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Answers (1)

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Rojas · Answer 1

33 years, 7 months

Step-by-step explanation:

Using the compound interest formula Accrued Amount = P (1 + r/n) ^ (nt)

where Accrued amount (A) is the expected future balance

A = $8000

P = principal; $5000

r = 1.4% = 0.014

t = number of years

n = number of times interest is compounded = 12 for monthly

Therefore

8000 = 5000 (1 + 0.014/12) ^ (12t)

Therefore

(1.001167) ^12t = 8000/5000

(1.001167) ^12t = 1.6

finding the log of both sides

12t x log 1.001167 = log 1.6

12t = log 1.6 / log 1.001167

12t = 402.98

t = 402.98/12

t = 33.58

hence time to increase the balance is 33 years, 7 months