Question

1. At 8% compounded annually, how long will it take $750 to double?1PT

2. At what rate must $400 be compounded annually for it to grow to $716.40 in 10 years? 1PT

3. A friend plans to buy a big-screen TV/entertainment system and can afford to set aside $1,320 toward the purchase today. If your friend can earn 5.0%, compounded yearly, how much can your friend spend in four years on the purchase?1PT

4. You just purchased a parcel of land for $10,000. If you expect a 12% annual rate of return on your investment, how much will you sell the land for in 10 years?1PT

5. If you place $50 in a savings account with an interest rate of 7% compounded annually, what will the investment be worth at the end of five years?1PT

Answer 1

Answer :1) Calculation of Number of Years :

Number of years = [ln(Future Value / Present Value)] / [ln (1 + rate)]

= [ln(1500 / 750)] / [ln(1 + 0.08)]

= ln (2) / ln (1.08)

= 0.69315 / 0.07696

= 9.00662681912 or 9 years

Answer :2) Calculation of Rate of Interest :

Future Value = Present Value * (1 + rate)^n

where Future Value = 716.40

Present Value = 400

n is number of years i.e 10

716.40 = 400 * (1 + rate)^10

Rate = [716.40 / 400] ^(1/10) - 1

On solving

Rate is 6%

Answer : 3) Calculaof Amount to be spent after Four years

Amount = Principal * (1 + rate)^number of years

= 1320 * (1 + 0.05)^4

= 1320 * 1.21550625

= 1604.46825 or 1604.47

Answer : 4) Calculation of Amount received on Land sell :

Amount = Principal * (1 + rate)^number of years

= 10000 * (1 + 0.12)^10

= 10000 * 3.105848

= 31058.48

Answer :5) Calculation of Amount in 5 years

Amount = Principal * (1 + rate)^number of years

= 50 * (1 + 0.07)^5

= 50 * 1.4025517307

= 70.13