금리 계산법

단리이자 계산 (Simple Interest)

I=PRT, where

P is the amount invested or borrowed,

R is the percentage rate of interest, i.e. R = r/100,

T is the time period of the investment or loan, in years.

Q1

(a) Calculate the simple interest earned on an investment of $350.00 at 6% p.a. over 7 years.

(b) Find the total balance of the account after 7 years.

Q2. Calculate the amount of simple interest that must be paid on a loan of $400.00 at 5.4% p.a. simple interest over 7 months.

복리이자 계산 (Compound Interest)

A=P(1+R)ⁿ, where

P is the principal, or amount invested

R is the interest rate per time period, expressed as a decimal

n is the number of time periods

A is the valuse of the investment after n time period

Q3. Peter invested $20 000.00 at 7% p.a. compound interest, with interest compounding annually. Find

(a) the value of this investment after 4 years

(b) the amount of interest earned

Q4. A sum of $10 000.00 is invested at 8% p.a. compound interest. Find the value of this investment after 3 years if the interest is compound

(a) half-yearly

(b) quarterly

SOLUTIONS

Q1.

(a) P=350, R=6/100=0.06, T=7

I=PRT=$350x0.06x7=$147. Therefore, the simple interest earned is $147.00

(b) Balance=principal+interest=350+147=$497. Thus, the amount od interest earned is $497.00

Q2. P=400, R=5.4/100=0.054, T=7/12 (since the time must be given in years and 7 months is 12/7 of a year)

I=PRT=400x0.054x7/12=$12.60 Thus, the simple interest paid over 7 months is $12.60

Q3

(a) P=20 000, R=0.07, n=4

A=P(1+R)ⁿ=20 000(1+0.07)⁴=26 215.92 Therefore, the value of this investment after 4 years is approximately $26 215.92

(b) 26 215.92-.92 Thus, the amount of interest earned is $6215.92

Q4 The amount does not compound anually. Therefore, we need to adjust the interest rate, R, and the number of time periods, n.

(a) The interest compunds every 6 months. The annual interest rate of 8% p.a. is equivalent to a rate of 4% every 6 months. Interest is paid twice a year for 3 years, therefore there are 6 time periods.

P=10 000, RT=0.04, n=6

A=P(1+R)ⁿ=10 000(1+0.04)^6≒12 653.19

Thus the interest compounded half yearly after 3 years is approximately $12 653.19

(b) The interest compounds every 3 months. The annual interest rate of 8% p.a. is equivqalent to a rate of 2% every 3 months. Interest is paid 4 times a year for 3 years, therefore there are 12 time periods.

P=10 000, R=0.02, n=12

A=P(1+R)ⁿ=10 000(1+0.02)^12≒12 682.42