Question

1. If the nominal interest rate of is 2% per quarter, what is the nominal rate per year ? 2. $100 of interest is paid each month on an investment of $10000, if the interest is compounded monthly at the end of 2 years, what is the accumulation at the end of two years ? 3. An individual wishes to deposit an amount of money now to have an accumulation of $500 at the end of five years. If the interest rate is at 4% per year, compounded semiannually, determine how much should be deposited ? 4. A sum of $1,000 deposited at time “O” at an interest rate of 5.5 % per year compounded quarterly for 5 years, how much is the future worth of the deposit

Answer 1

(1)

Nominal interest rate per quarter = 2%

Nominal interest rate per year (2*4) = 8%

(2)

Interest on investment of each month = $100

Investment = $100,000

Rate of interest per month = 100/100000*100

=0.1% per month

Interest compounded monthly

Time = 2 years

2*12 = 24 months

Accumulation at the end of 2 year

= 100,000(1+0.1/100)^24

= 100,000(1.001)^24

= 100,000*1.02428

= $102,428

(3)

Accumulation at the end of 5 years = $500

Interest rate = 4% per year, compounded semiannually

Interest rate (4/2) = 2% semiannually

Time = 5 years

5*2 = 10 half year

Determine how much should be deposited

Let X amount is deposited

500 = X(1+2/100)^10

500/X = (1.02)^10

500/x = 1.2190

X = 500/1.2190

X = 410 approx

Let's check the answer

410(1+2/100)^10

= 410*1.2190

= 499 75

= $500 approx

Hence amount deposited = $410

(4)

Sum deposited =$1,000

Interest rate = 5.5% per year, compounded quarterly

Interest rate quarterly (5.5/4) = 1.375%

Time= 5 years

Time (5*4) = 20 quarters

Future worth = 1000(1+1.375/100)^20

= 1000(1.01375)^20

= 1000*1.314

= $1,314 approx

Thank you :)