Question

1)What is the value of an ordinary annuity at the end of 20 years if $16,500 is deposited each year into an account earning 8.5% compound annually? How much of this value is interest?

2) How long will it take an investment of $5000 to triple if the investment earns interest at the rate of 5%/year compounded daily?

3) What is the effective rate of money invested at 4.5% compunded semi-annuallY?

Answer 1

Answer 1.

Annual Deposit = $16,500
Annual Interest Rate = 8.5%
Period = 20 years

Accumulated Sum = $16,500*1.085^19 + $16,500*1.085^18 + … + $16,500*1.085 + $16,500
Accumulated Sum = $16,500 * (1.085^20 - 1) / 0.085
Accumulated Sum = $16,500 * 48.3770
Accumulated Sum = $798,220.50

Value of an ordinary annuity at the end of 20 years is $798,220.50

Answer 2.

Amount Invested = $5,000
Desired Sum = $15,000
Annual Interest Rate = 5%
Daily Interest Rate = 5%/365 = 0.0137%

Let $5,000 will grow to $15,000 in ‘n’ days

$5,000 * 1.000137^n = $15,000
1.000137^n = 3
n * ln(1.000137) = ln(3)
n = 8019.62 days

Number of days = 8,019.62
Number of years = 21.97 years

Answer 3.

Annual Interest Rate = 4.5%
Semiannual Interest Rate = 2.25%

Effective Rate of Interest = (1 + Semiannual Interest Rate)^2 - 1
Effective Rate of Interest = 1.0225^2 - 1
Effective Rate of Interest = 1.0455 - 1
Effective Rate of Interest = 0.0455 = 4.55%