Question

A person borrows $200 to be repaid in 8 years with 14% annually compounded interest. The loan may be repaid at the end of any earlier year with no prepayment penalty.
a. What amount will be due if the loan is repaid at the end of year 1?
b. What is the repayment at the end of year 4?
c. What amount is due at the end of the eighth year?

Answer 1

Answer:

Explanation:

Borrow amount =$200

Therefore principal =$200

Time 8years

Rate 14% per an um. Compound

1. Payment due at end of the first year i.e at t=1

Compound interest is given as,

A=P(1+r/n)^nt

A= amount

P= principal

r= rate

n = number of time the interest is compound, in this case it will be 1 because we are not told if is monthly.

t= time

A=P(1+r/n)^nt

A=200(1+0.14/1)^1×1

A=200(1+0.14)^1

A=200(1.14/1)^1

A=200×1.14

A=$228

2. The repayment after four years i.e at t=4

A=P(1+r/n)^nt

A=200(1+0.14/1)^4×1

A=200(1+0.14)⁴

A=200(1.14/1)⁴

A=200×1.14⁴

A=$337.79

3. At the end of 8years

t=8

A=P(1+r/n)^nt

A=200(1+0.14/1)^8×1

A=200(1+0.14)^8

A=200(1.14/1)^8

A=200×1.14^8

A=$570.52.

Answer 2

Answer:

Explanation:

The formula to be used in calculation is FV = PV*(1+I)^n

FV - Future value at the end of periods

PV - Present value

r - interest rate

n - number of years

a. The amount due f the loan is repaid at the end of year 1

FV = 200*(1+0.14)^1 = 200*0.14 = $228

b. Repayment at the end of year 4

FV = 200*(1+0.14)^4 = 200* 1.6889 = $337.79

c. The amount due at the end of 8 year

FV = 200*(1+0.14)^8 = 200* 2.85 = $570.51