Calculate the future value of an investment using simple interest and compound interest (annually and…

Question

Calculate the future value of an investment using simple interest and compound interest (annually and quarterly).

ScanSolve AI Tutor · Accepted Answer

Here's the solution to question 1. Given: Principal (P) = N250000; Interest rate (r) = 15% = 0.15; Time (t) = 15 years a) Simple interest The formula for simple interest is A = P(1 + rt). Step 1: Substitute the given values into the formula. A = 250000(1 + 0.15 × 15) Step 2: Calculate the product of r and t. A = 250000(1 + 2.25) Step 3: Add the values inside the parenthesis. A = 250000(3.25) Step 4: Multiply to find the final amount. A = 812500 The amount after 15 years with simple interest is N812500.00. b) Interest compounded: The formula for compound interest compounded n times per year is A = P(1 + r/n)^(nt). The formula for compound interest compounded continuously is A = Pe^(rt). i. annually For annual compounding, n=1. Step 1: Substitute the values into the formula. A = 250000(1 + 0.15/1)^(1 × 15); A = 250000(1.15)¹⁵ Step 2: Calculate (1.15)¹⁵. A = 250000 × 8.1370619 Step 3: Multiply to find the final amount. A = 2034265.475 The amount after 15 years compounded annually is N2034265.48. ii. quarterly For quarterly compounding, n=4. Step 1: Substitute the values into the formula. A = 250000(1 + 0.15/4)^(4 × 15); A = 250000(1 + 0.0375)⁶⁰; A = 250000(1.0375)⁶⁰ Step 2: Calculate (1.0375)⁶⁰. A = 250000 × 9.429007 Step 3: Multiply to find the final amount. A = 2357251.75 The amount after 15 years compounded quarterly is N2357251.75. iii. semi-annually For semi-annual compounding, n=2. Step 1: Substitute the values into the formula. A = 250000(1 + 0.15/2)^(2 × 15); A = 250000(1 + 0.075)³⁰; A = 250000(1.075)³⁰ Step 2: Calculate (1.075)³⁰. A = 250000 × 8.75699 Step 3: Multiply to find the final amount. A = 2189247.5 The amount after 15 years compounded semi-annually is N2189247.50. iv. continuously For continuous compounding, the formula is A = Pe^(rt). Step 1: Substitute the values into the formula. A = 250000 × e^(0.15 × 15); A = 250000 × e^(2.25) Step 2: Calculate e^(2.25). A = 250000 × 9.487735 Step 3: Multiply to find the final amount. A = 2371933.75 The amount after 15 years compounded continuously is N2371933.75.

Calculate the future value of an investment using simple interest and compound interest (annually and quarterly).

Answers

Step-by-step solution

Part a· 4 steps

Substitute the given values into the formula.

Calculate the product of $r$ and $t$ .

Add the values inside the parenthesis.

Multiply to find the final amount.

Part b(i)· 3 steps
$\text{N}2034265.48$

Substitute the values into the formula.

Calculate $(1.15)^{15}$ .

Multiply to find the final amount.

Part b(ii)· 3 steps
$\text{N}2357251.75$

Substitute the values into the formula.

Calculate $(1.0375)^{60}$ .

Multiply to find the final amount.

Part b(iii)· 3 steps
$\text{N}2189247.50$

Substitute the values into the formula.

Calculate $(1.075)^{30}$ .

Multiply to find the final amount.

Part b(iv)· 3 steps
$\text{N}2371933.75$

Substitute the values into the formula.

Calculate $e^{2.25}$ .

Multiply to find the final amount.

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More Mathematics Questions

Calculate the future value of an investment using simple interest and compound interest (annually and quarterly).

Answers

Step-by-step solution

Part a· 4 steps

Substitute the given values into the formula.

Calculate the product of rrr and ttt.

Add the values inside the parenthesis.

Multiply to find the final amount.

Part b(i)· 3 stepsN2034265.48\text{N}2034265.48N2034265.48

Substitute the values into the formula.

Calculate (1.15)15(1.15)^{15}(1.15)15.

Multiply to find the final amount.

Part b(ii)· 3 stepsN2357251.75\text{N}2357251.75N2357251.75

Substitute the values into the formula.

Calculate (1.0375)60(1.0375)^{60}(1.0375)60.

Multiply to find the final amount.

Part b(iii)· 3 stepsN2189247.50\text{N}2189247.50N2189247.50

Substitute the values into the formula.

Calculate (1.075)30(1.075)^{30}(1.075)30.

Multiply to find the final amount.

Part b(iv)· 3 stepsN2371933.75\text{N}2371933.75N2371933.75

Substitute the values into the formula.

Calculate e2.25e^{2.25}e2.25.

Multiply to find the final amount.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Calculate the product of $r$ and $t$ .

Part b(i)· 3 steps
$\text{N}2034265.48$

Calculate $(1.15)^{15}$ .

Part b(ii)· 3 steps
$\text{N}2357251.75$

Calculate $(1.0375)^{60}$ .

Part b(iii)· 3 steps
$\text{N}2189247.50$

Calculate $(1.075)^{30}$ .

Part b(iv)· 3 steps
$\text{N}2371933.75$

Calculate $e^{2.25}$ .