Question

Find the present value and compound interest.compound amount =20,000nominal rate= 6%terms of loan= 10 yearsinterest compounded=annually

Answer 1

Using the compound interest formula, we have found out that the present value is 1168 and the compound interest is 241765163.

It is given to us that -

The compound amount = 20,000

Nominal rate = 6%

Terms of loan = 10 years

The amount is compounded annually.

We have to find out -

The present value

and, the Compound Interest

Firstly, we have to find out the Effective Annual Interest Rate. The formula for Effective Annual Interest Rate is -

$Effective Annual Interest Rate = (1+\frac{i}{n}) ^{n} -1$ ----- (1)

where, $i$ = Nominal Interest rates

and, $n$ = Number of periods

Thus, from equation (1), we can find the Effective Annual Interest Rate -

$Effective Annual Interest Rate = (1+\frac{i}{n}) ^{n} -1\\= (1+\frac{6}{10}) ^{10} -1\\= (\frac{16}{10} )^{2} -1\\= 2.56-1\\=1.56$

Thus, the Effective Annual Interest Rate is 1.56.

Now, we know, the formula of Compound Interest is -

$Compound Interest = P * (1+r)^{t} - P$ ----- (2)

where, P = Principal amount

r = Annual Interest rate

t = Number of years for which the interest is applied

Thus, taking the value of r as 1.56 from Effective Annual Interest Rate and from equation (2), we can find the Compound Interest -

$Compound Interest = P * (1+r)^{t} - P\\= 20000* (1+1.56)^{10} - 20000\\= 20000*12090 - 20000\\= 241785163-20000\\=241765163$

Thus, the Compound Interest is 241765163.

Now, to find the Present Value, we have to use the formula of Present Value that can be represented as -

$Present Value = \frac{FV}{(1+\frac{r}{n} )^{nt} }$ ---- (3)

where, FV = Future Value

r = Rate of interest

n = number of times the amount is compounding. In this case n=1 since the amount is compounded annually

t = Time in years

Thus, from equation (3), the Present Value can be calculated as -

$Present Value = \frac{FV}{(1+\frac{r}{n} )^{nt} }\\= \frac{241765163}{(1+\frac{6}{1} )^{1*10} }\\= \frac{241765163}{282475249}\\=1168$

Thus, the present value is 1168.

Using the compound interest formula, we have found out that the present value is 1168 and the compound interest is 241765163.

To learn more about compound interest visit https://brainly.com/question/14295570

#SPJ9